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"text": "Computer Graphics: Why & What? Why How does a water softener work? by Nicholas Gerbis - \"A Picture is Worth a f share yTweet 89 8-1 33 Page 12 3 Thousand Words\" howstuffw?rks.com Quickc Whaf's hard and scaly and dwells in your pipes?No,its not the pet alligator your parents flushed down the toilet-he's grown up and Brain terrorizing the sewers of Chicago.We're talking about hard water. Stuff We call water hardir it contains a lot of calcium magnesium or other minerals.Groundwater withMarshall Brain acquires these metals by dissolving them frorm Water Softner surrounding soil and rock.Industry measures water hardness in terms of grains per gallon GPGor mlligrams per iermg/L.A grain is defined as64.8miligrams of calcium carbonate Watch as Marehall Brain cxplaina howwater softenere work source:Business Dictionary.I your water tests brainstutr at 1GPG17.1mg/L) or less,then you have soft water.Water around 1-35GPG17.1-60 mg/L) UP NEXT ocoupies a gray zone between soft and slightly How Home Dry Cleaning Works hard water and 3.5-7GPG60-120 mg/L) is How the Toto Washiet Works moderately hard.Hard water is around7-10.5 10 Stand-up Facts About Wateriess Urinals GPG120-180mg/L)and very hardwater is above that [source:Water Quality Association] How do all those number affect you?Hard water causes two problems 1.Dissolved calcium and magnesium precipltate out of hard water as scale,which builds up on the insides of pipes,water heaters,tea kettles,coffee makers and industrial machineryScale reduces flow through pipes and is a poor conductor of heat.Eventually.pipes can become completely clogged. 2.Hard water reduces soap's abllty to lather,whether in the shower,sink,dishwasher or washing machine.and reacts witn soap to form a sticky scum Science and Engineering - HCMUT Faculty of Computer Slide 3",
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"text": "Further Reading \"Interactive Computer Graphics: A Topdown Approach Using OpenGL\", Edward Ange/ - Chapter 1: Graphics Systems And Models \"D hoa máy tinh trong khng gian hai chiéu\", Trán Giang Son - Chu'ong 1: Gi6i thieu d hoa máy tinh Faculty of Computer Science and Engineering - HCMUT Slide 61",
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"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 02: Graphics Programming tgson@hcmut.edu.vn",
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"text": "Introduction Programming Environment - Hardware: display, graphics card - Software: Os (Windows), programming language (MS VC++), graphics library (OpenGL, DirectX) OpenGL - Platform-independent API - Easy to use - Close enough to the hardware to get excellent performance - Treat 2D and 3D in the same way Faculty of Computer Science and Engineering - HCMUT Slide 3",
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"text": "OpenGL Libraries OpenGL core library - OpenGL32 on Windows - GL on most unix/linux systems (libGL.a) OpenGL Utility Library (GLU) - Provides functionality in OpenGL core but avoids having to rewrite code Links with window system - GLX for X window systems - WGL for Windows - AGL for Macintosh Faculty of Computer Science and Engineering - HCMUT Slide 4",
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"text": "OpenGL Libraries OpenGL File Home Share View 1 ThisPC > NewVolumeD: Software OpenGL > OpenGL V Name Date modified Type Size Quick access glut-3.spec 2/26/201012:11PM WPSPDFDocume... 404 KB Desktop X OPENGL32 5/13/19983:00PM Object File Library 76 KB Downloads 808 gut32 11/8/20015:27PM Object File Library 29 KB Documents 808 GLU32 5/13/19983:00PM Object File Library 13 KB Pictures glut 12/13/20003:22PM C/C++ Header 28 KB Chuong 1 GLU 4/24/19983:00PM C/C++ Header 18 KB GLAUX 4/24/19983:00PM C/C++ Header 12 KB Chuong 1 GL 4/24/19983:00PM C/C++ Header 68 KB Chuong 2 opengl32.dll 8/4/20049:07AM Application exten... 697 KB Work gut32.dll 11/8/20015:27PM Application exten... 232 KB OneDrive glu32.dll 8/4/20049:07AM Application exten... 120 KB This PC 3D Objects Desktop Documents Faculty of Computer Science and Engineering - HCMUT Slide 5",
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"text": "OpenGL Libraries ?x New Files Projects Workspaces Other Documents ATL COM AppWizard Project name: wClusterResource Type Wizard Test CustomAppWizard Database Project Logation: aDevStudioAdd-in Wizard E:LecturesDohoamaytinhCG usi lSAPl Extension Wizard Makefile acMFCActiveXControlWizard MFC AppWizard(dll) C \"E:LecturesDohoamaytinhCG using OpenGLExamplesChapter 2Te. MFCAppWizard(exe) Tf Utility Project Hello aWin32Applicatior Press any key to continue Win32 Console Application &Win32Dynamic-LinkLibrary Win32StaticLibrary Faculty of Computer Science and Engineering - HCMUT Slide 7",
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"text": "OpenGL Libraries Visual Studio Edit program.h Notepad program.c (cpp) C:Program FilesMicrosoft SDKs gl/gl.h Compile Windowsv7.0AIncludegl gl/glu.h program.ob C:Program FilesMicrosoft SDKs Link opengl32.lib Windowsv7.0ALib program.exe Faculty of Computer r Science and Engineering - HCMUT Slide 10",
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"text": "OpenGL Libraries Use registry to lookup driver name: HKEY LOCAL MACHINE/ System/CurrentControlSet/ Control/Class/ program.exe {Adapter GUID}/0000/ OpenglDriverName If graphics card installed nvoglv32.dll opengl32.dll (Opengl: hardware acceleration) (Opengl: software implementation) : Graphics Card from NVIDIA C:WindowsSystem32 C:WindowsSystem32 Operating System: Windows Faculty of Computer Science and Engineering - HCMUT Slide 11",
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"text": "Windows-based programming Event Queue e t This PC Microsoft Firefox Edge Calculator X I Programmer Recycle Bin Viber MonkeySt. 0 HEX 0 Control WPSPDF Adobe DEC 0 Panel Creati... OCT 0 BIN 0 W QWORD MS ?C Foxit Reader WPS Home DBitwise Bit Shift CREDIBLE Presentation File View 0 E... >> c & S Clipboard Image Tools Brushes Shapes Size Colors Edit with Paint 3D ) % : Google WPS Chrome Spreadsheets 7 8 9 X W 4 5 6 TeamViewer WPSWriter 1 2 3 + 14 +/ 0 Zalo n t UniKey Zalo + 100% 1 e a P3 ENG 3:05PM 3/7/2020 Faculty of Computer r Science and Engineering - HCMUT Slide 14",
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"text": "Windows-based programming Event Queue e t This PC Microsoft Firefox Edge Calculator X Programmer Recycle Bin Viber MonkeySt. 0 HEX 0 Control WPSPDF Adobe DEC 0 Panel Creati... OCT 0 BIN 0 W QWORD MS ?C Foxit Reader WPS Home :D Bitwise Bit Shift CREDIBLE Presentation File View 0 E... >> c & Clipboard Image Tools Brushes Shapes Size Colors Edit with Paint 3D ) % : Google WPS Chrome Spreadsheets 7 8 9 X W 4 5 6 TeamViewer WPSWriter 1 2 3 + 14 +/ 0 Zalo n t UniKey Zalo + 100% 1 e a P3 ENG 3:05PM 3/7/2020 Faculty of Computer r Science and Engineering - HCMUT Slide 16",
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"text": "Viewing glBegin(GL_POLYGON) simple glVertex2f(-0.5, -0.5): glVertex2f(-0.5, 0.5) glVertex2f(0.5, 0.5); glVertex2f(0.5, -0.5): gEndO 1 1 -1 Faculty of Computer r Science and Engineering - HCMUT Slide 24",
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"text": "Viewing glBegin(GL_POLYGON)) H start glVertex2f(1.0, 1.0); glVertex2f(1.0, 2.0); glVertex2f(2.0, 2.0); glVertex2f(2.0, 1.0): gEndO 1 1 -1 Faculty of Computer r Science and Engineering - HCMUT Slide 25",
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"text": "Viewing glBegin(GL_POLYGON) start glVertex2f(0.5, 0.5); glVertex2f(0.5, 1.5) glVertex2f(1.5, 1.5); glVertex2f(1.5, 0.5): gEndO 1 -1 1 -1 Faculty of Computer r Science and Engineering - HCMUT Slide 26",
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"id": "CO3059-chapter-2-slide-087-0000",
"text": "Viewing glMatrixMode (GL_PROJECTION); glLoadldentity0; gl0rtho(-1.0, 1.0, -1.0, 1.0, -1.0, 1.0): gIMatrixMode (GL_PROJECTION); glLoadldentity0; gl0rtho(-1.0, 1.0, -1.0, 1.0) glOrtho(left, right, bottom, top, near, far) gluOrtho2D(left, right,bottom,top) Faculty of Computer Science and Engineering - HCMUT Slide 27",
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"text": "Viewing 2 - 1 -2 4 -4 Faculty of Computer s Science and Engineering - HCMUT Slide 28",
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"id": "CO3059-chapter-2-slide-089-0000",
"text": "Viewing glBegin(GL_POLYGON)) glVertex2f(-2.0, 0.0); glVertex2f(-2.0, 2.0): glVertex2f(0.0, 2.0); glVertex2f(0.0, 0.0) glEndO: glBegin(GL_POLYGON) glVertex2f( 0.0, -4.0); glVertex2f( 2.0, 0.0); glVertex2f( 4.0, -4.0); gEndO Faculty of Computer Science and Engineering - HCMUT Slide 29",
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"id": "CO3059-chapter-2-slide-090-0000",
"text": "Viewing How to get the picture of triangle and square? start [N.. An 2 -2 4 .4 Faculty of Computer r Science and Engineering - HCMUT Slide 30",
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"text": "Viewing How to get the picture of triangle and square? glMatrixMode (GL_PROJECTION); glLoadldentityO; gluOrtho2D(-2.0, 4.0, -4.0, 2.0 How to get the picture of the square? How to get the picture of the triangle? Faculty of Computer Science and Engineering - HCMUT Slide 31",
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"text": "Viewport Do not have use the entire window for the image: glViewport(x,y,w,h Viewport h x w Graphics window y Clipping window Faculty of Computer r Science and Engineering - HCMUT Slide 32",
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"CO3059-chapter-2-slide-094-0000": {
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"text": "Viewport glViewport(320, 240, 320, 240) start N. An Faculty of Computer Science and Engineering - HCMUT Slide 34",
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"CO3059-chapter-2-slide-095-0000": {
"id": "CO3059-chapter-2-slide-095-0000",
"text": "Viewport glViewport(320, 240, 240, 240) start An. Faculty of Computer Science and Engineering - HCMUT Slide 35",
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"CO3059-chapter-2-slide-096-0000": {
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"text": "Viewport How to draw picture in the second quadrant? start Viet. An. 3M Faculty of Computer r Science and Engineering - HCMUT Slide 36",
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"text": "Viewport How to draw picture in the second quadrant? - glViewport(0,240, 320, 240) How to draw picture in the third quadrant? How to draw picture in the fourth quadrant? How to draw picture in all quadrant? Faculty of Computer Science and Engineering - HCMUT Slide 37",
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"text": "Viewport glViewport(320, 240, 320, 240) glBegin( //draw square gEnd0 glBegin0 //draw triangle gEndO glViewport(0, 240, 320, 240 glViewport(0, 0, 320, 240): glViewport(320, 0, 320, 240 Faculty of Computer Science and Engineering - HCMUT Slide 39",
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"CO3059-chapter-2-slide-100-0000": {
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"text": "Primitives - Objects - Viewer Light Source(s) - Materials Polyline Filled region Text Raster image Faculty of Computer Science and Engineering - HCMUT Slide 40",
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"CO3059-chapter-2-slide-101-0000": {
"id": "CO3059-chapter-2-slide-101-0000",
"text": "Primitives D Polyline - A polyline is a connected sequence of straight lines - A polyline can be used to approximated a smooth curve Faculty of Computer Science and Engineering - HCMUT Slide 41",
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"id": "CO3059-chapter-2-slide-102-0000",
"text": "Primitives Polyline - Polygon: polyline if the first and the last points are connected by an edge - Polygon type: simple, convex Faculty of Computer r Science and Engineering - HCMUT Slide 42",
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"CO3059-chapter-2-slide-103-0000": {
"id": "CO3059-chapter-2-slide-103-0000",
"text": "Primitives Polyline - Attributes: Color, thickness, type (solid, dash), join points Faculty of Computer Science and Engineering - HCMUT Slide 43",
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"text": "Primitives Filled region - Filled region is a shape filled with some color or pattern. The boundary is often a polygon A B D C Faculty of Computer Science and Engineering - HCMUT Slide 44",
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"CO3059-chapter-2-slide-105-0000": {
"id": "CO3059-chapter-2-slide-105-0000",
"text": "Primitives dimensional object Faculty of Computer r Science and Engineering - HCMUT Slide 45",
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"id": "CO3059-chapter-2-slide-106-0000",
"text": "Primitives Text Vy=Vxsin-gt Vx=Vxcos V·sin-t-/gt R41.59 Faculty of Computer Science and Engineering - HCMUT Slide 46",
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"text": "Primitives Text: - Attributes: Font, color, size, orientation, space Arial Arial bold Afiaf itaffc Times Times Bold Tmes italic Courier Courier Courie Faculty of Computer Science and Engineering - HCMUT Slide 47",
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"id": "CO3059-chapter-2-slide-109-0000",
"text": "Draw Object glBegin(parameter) glVertex2f(...) //or glVertex3f(...) glVertex2f(...) gEndO Parameter - GL POINTS, GL LINES,GL TRIANGLES, V.V Faculty of Computer Science and Engineering - HCMUT Slide 49",
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"text": "Draw Object gIBegin(GL_POINTS); start glVertex2f(-0.5, 1.0) glVertex2f( 0.5, 1.0) glVertex2f(-0.5, 0.0): glVertex2f( 0.5, 0.0) glVertex2f(-0.5, -1.0): glVertex2f( 0.5, -1.0); gEndO Faculty of Computer r Science and Engineering - HCMUT Slide 50",
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"text": "Draw Object H start gIBegin(GL_LINES); glVertex2f(-0.5, 1.0) glVertex2f( 0.5, 1.0) glVertex2f(-0.5, 0.0): glVertex2f( 0.5, 0.0) glVertex2f(-0.5, -1.0) glVertex2f( 0.5, -1.0); gEndO Faculty of Computer r Science and Engineering - HCMUT Slide 51",
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"text": "Draw Object gIBegin(GL_LINE_STRIP); H start glVertex2f(-0.5, 1.0) glVertex2f( 0.5, 1.0) glVertex2f(-0.5, 0.0): glVertex2f( 0.5, 0.0) glVertex2f(-0.5, -1.0): glVertex2f( 0.5, -1.0) gEndO Faculty of Computer r Science and Engineering - HCMUT Slide 52",
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"id": "CO3059-chapter-2-slide-113-0000",
"text": "Draw Object gIBegin(GL_LINE_LOOP); H start glVertex2f(-0.5, 1.0); glVertex2f( 0.5, 1.0) glVertex2f(-0.5, 0.0): glVertex2f( 0.5, 0.0) glVertex2f(-0.5, -1.0): glVertex2f( 0.5, -1.0) gEndO Faculty of Computer r Science and Engineering - HCMUT Slide 53",
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"CO3059-chapter-2-slide-114-0000": {
"id": "CO3059-chapter-2-slide-114-0000",
"text": "Draw Object glBegin(GL_TRIANGLES) H start glVertex2f(-0.5, 1.0); glVertex2f( 0.5, 1.0) glVertex2f(-0.5, 0.0): glVertex2f( 0.5, 0.0) glVertex2f(-0.5, -1.0): glVertex2f( 0.5, -1.0) gEndO Faculty of Computer r Science and Engineering - HCMUT Slide 54",
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"CO3059-chapter-2-slide-115-0000": {
"id": "CO3059-chapter-2-slide-115-0000",
"text": "Draw Object gIPolygonMode(GL_FRONT_AND_BACK,GL_LINE); glColor3f(1.0, 0.0, 0.0) glLineWidth(3.0 start H start Faculty of Computer Science and Engineering - HCMUT Slide 55",
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"CO3059-chapter-2-slide-116-0000": {
"id": "CO3059-chapter-2-slide-116-0000",
"text": "Draw Object gIPolygonMode(GL_FRONT_AND_BACK,GL_POINT); glColor3f(1.0, 1.0, 0.0) glPointSize(5); start Faculty of Computer r Science and Engineering - HCMUT Slide 56",
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"CO3059-chapter-2-slide-117-0000": {
"id": "CO3059-chapter-2-slide-117-0000",
"text": "Draw Object gIPolygonMode(GL_FRONT_AND_BACK,GL_FILL) glColor3f(0.0, 1.0, 0.0) glClearColor(1.0, 1.0, 1.0, 1.0); start Faculty of Computer r Science and Engineering - HCMUT Slide 57",
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"CO3059-chapter-2-slide-118-0000": {
"id": "CO3059-chapter-2-slide-118-0000",
"text": "Draw Object H start Faculty of Computer Science and Engineering - HCMUT Slide 58",
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"CO3059-chapter-2-slide-119-0000": {
"id": "CO3059-chapter-2-slide-119-0000",
"text": "Draw Object gIPolygonMode(GL_FRONT_AND_BACK,GL_FILL) glColor3f(0.0,1.0,0.0): glClearColor(1.0, 1.0, 1.0, 1.0); glBegin(GL_TRIANGLES): glEndO; gIPolygonMode(GL_FRONT_AND_BACK,GL_LINE); glColor3f(1.0, 0.0, 0.0) glLineWidth(3); glBegin(GL_TRlANGLES) glEndO Faculty of Computer Science and Engineering - HCMUT Slide 59",
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"CO3059-chapter-2-slide-120-0000": {
"id": "CO3059-chapter-2-slide-120-0000",
"text": "Draw Object glBegin(GL_TRIANGLES) H start glVertex2f(-0.5, 1.0); glVertex2f( 0.5, 1.0); glVertex2f(-0.5, 0.0) glVertex2f(-0.5, 0.0) glVertex2f( 0.5, 1.0); glVertex2f( 0.5, 0.0); glVertex2f(-0.5, -1.0)) glVertex2f(-0.5, 0.0): glVertex2f( 0.5, 0.0); glVertex2f( 0.5, 0.0); glVertex2f(-0.5, -1.0) glVertex2f( 0.5, -1.0) glEndO; Faculty of Computer r Science and Engineering - HCMUT Slide 60",
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"CO3059-chapter-2-slide-121-0000": {
"id": "CO3059-chapter-2-slide-121-0000",
"text": "Draw Object clip eye normalized window coordinates coordinates device coordinates coordinates VM P clip V(V2...- modelview projection perspective viewport matrix matrix division matrix Faculty of Computer Science and Engineering - HCMUT Slide 61",
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"CO3059-chapter-2-slide-122-0000": {
"id": "CO3059-chapter-2-slide-122-0000",
"text": "Draw Object glBegin(GL_TRIANGLE_STRIP): H start glVertex2f(-0.5, 1.0);//v1 glVertex2f( 0.5, 1.0);//v2 glVertex2f(-0.5, 0.0);//v3 glVertex2f( 0.5, 0.0);//v4 glVertex2f(-0.5, -1.0);//v5 glVertex2f( 0.5, -1.0);//v6 gEndO Faculty of Computer Science and Engineering - HCMUT Slide 62",
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"CO3059-chapter-2-slide-123-0000": {
"id": "CO3059-chapter-2-slide-123-0000",
"text": "Object Draw v1 v1 v2 v2 v3 v4 v3 v4 v5 v6 v5 v6 v2,v1,v4,v3,v6, v5 v1,v2,v3,v4,v5,v6 Faculty of Computer r Science and Engineering - HCMUT Slide 63",
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"CO3059-chapter-2-slide-124-0000": {
"id": "CO3059-chapter-2-slide-124-0000",
"text": "Draw Object GL QUADS, GL QUAD STRIP, GL TRIANGLE FAN GL POLYGON GL TRIANGLES GL TRIANGLE STRIP GL TRIANGLE FAN GL QUADS GL QUAD STRIP 6 Faculty of Computer Science and Engineering - HCMUT Slide 64",
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"CO3059-chapter-2-slide-125-0000": {
"id": "CO3059-chapter-2-slide-125-0000",
"text": "Draw Object void drawPoint(GLint x,GLint y) { glBegin(GL_POINTS); glVertex2i(x, y): glEndO void drawLine(GLint x1, GLint y1,GLint x2,GLint y2){ gIBegin(GL_LINES); glVertex2i(x1,y1) glVertex2i(x2,y2) glEndO Faculty of Computer Science and Engineering - HCMUT Slide 65",
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"CO3059-chapter-2-slide-126-0000": {
"id": "CO3059-chapter-2-slide-126-0000",
"text": "The Sierpinski Gasket Sierpinski gasket Po p Faculty of Computer Science and Engineering - HCMUT Slide 66",
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"CO3059-chapter-2-slide-127-0000": {
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"text": "The Sierpinski Gasket Pick an initial point (x, y, z) at random inside the triangle 1. 2. Select one of the three vertices at random 3. Find the location halfway between the initial point and the randomly selected vertex 4. Display this new point by putting some sort of marker, such as a small circle at the corresponding location on the display 5. Replace the point at (x, y, z) with this new point 6. Return to step 2 Faculty of Computer Science and Engineering - HCMUT Slide 67",
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"CO3059-chapter-2-slide-128-0000": {
"id": "CO3059-chapter-2-slide-128-0000",
"text": "The Sierpinski Gasket maino Initialize the_systemO for(some_number_of_points) pt = generate_a_pointO Display_the_point(pt): Faculty of Computer Science and Engineering - HCMUT Slide 68",
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"CO3059-chapter-2-slide-129-0000": {
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"text": "The Sierpinski Gasket void myinit( glClearColor(1.0, 1.0, 1.0, 1.0); /* white background */ glColor3f(1.0, 0.0, 0.0); /* draw in red */ glMatrixMode(GL_PROJECTlON): glLoadldentityO; gluOrtho2D(0.0, 50.0, 0.0, 50.0); glMatrixMode(GL_MODELVlEW); Faculty of Computer Science and Engineering - HCMUT Slide 69",
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"CO3059-chapter-2-slide-130-0000": {
"id": "CO3059-chapter-2-slide-130-0000",
"text": "The Sierpinski Gasket void display( void ){ GLfloat vertices[3][2]={{0.0,0.0},{25.0,50.0},{50.0,0.0}}; /* A triangle */ int j, k; srand(time(NULL)); /* standard random number generator */ GLfloat p[2] ={7.5,5.0}; /* An arbitrary initial point inside traingle */ glClear(GL_COLOR_BUFFER BlT); /*clear the window */ glBegin(GL_POINTS); for(k=0;k<5000;k++){ j = randO%3; /* pick a vertex at random */ p[0] = (p[0]+vertices[j][0]/2.0 p[1] = (p[1]+vertices[j][1]/2.0 glVertex2fv(p); glEndO; glFlushO; /* clear buffers */ Faculty of Computer Science and Engineering - HCMUT Slide 70",
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"CO3059-chapter-2-slide-131-0000": {
"id": "CO3059-chapter-2-slide-131-0000",
"text": "Further Reading \"Interactive Computer Graphics: A Topdown Approach Using OpenGL\", Edward Ange/ - Chapter 2: Graphics Programming \"D hoa máy tinh trong khng gian hai chiéu\", Trán Giang Son - Chuong 2: Bu6c däu tao hinh änh \" hoa máy tinh trong khng gian ba chiéu\", Trán Giang Son - Chuong 1: M hinh hóa döi tu'ong ba chiéu bäng lu6i da giäc Faculty of Computer Science and Engineering - HCMUT Slide 71",
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"CO3059-chapter-3-slide-132-0000": {
"id": "CO3059-chapter-3-slide-132-0000",
"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 03: 3D Object & Mesh Trän Giang Son tgson@hcmut.edu.vn",
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"CO3059-chapter-3-slide-133-0000": {
"id": "CO3059-chapter-3-slide-133-0000",
"text": "OUTLINE Draw Sierpinski gasket by recursion Draw 3D Sierpinski gasket Hidden Surface Modeling Sphere Data Structure Faculty of Computer Science and Engineering - HCMUT Slide 2",
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"timestamp": "2025-10-31T22:21:19+07:00"
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"CO3059-chapter-3-slide-134-0000": {
"id": "CO3059-chapter-3-slide-134-0000",
"text": "The Sierpinski Gasket Start with a triangle Repeat Faculty of Computer Science and Engineering - HCMUT Slide 3",
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"CO3059-chapter-3-slide-135-0000": {
"id": "CO3059-chapter-3-slide-135-0000",
"text": "The Sierpinski Gasket Five subdivisions Faculty of Computer Science and Engineering - HCMUT Slide 4",
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"CO3059-chapter-3-slide-136-0000": {
"id": "CO3059-chapter-3-slide-136-0000",
"text": "The Sierpinski Gasket Glfloat v[3][2]={{-1.0, -0.58}, {1.0, -0.58}, {0.0, 1.15}}; int n; triangle( void Glfloat ai Glfloat *b, 1 Glfloat *c) /* display triangle one g1Vertex2fv(a); g1Vertex2fv(b); g1vertex2fv(c) ; 25 Faculty of Computer Science and Engineering - HCMUT Slide 5",
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"CO3059-chapter-3-slide-137-0000": {
"id": "CO3059-chapter-3-slide-137-0000",
"text": "The Sierpinski Gasket *b i void divide_triangle(GLfloat a Glfloat Glfloat *C, : int m) point2 v0, v1, v2; int j; if(m>0){ for(j=0; j<2; j++) v0[j]=(a[j]+b[j]/2; for(j=0; j<2; j++ v1[j]=(a[j]+c[j]/2; for(j=0; j<2; j++ v2[j]=(b[j]+c[j]/2; divide_triangle(a, , vo, v1, m-1); divide_triangle(c, v1, v2, n m-1); divide_triangle(b, v2, v0, m-1); 2 else(triangle(a,b,c)): 2 Faculty of Computer Science and Engineering - HCMUT Slide 6",
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"CO3059-chapter-3-slide-138-0000": {
"id": "CO3059-chapter-3-slide-138-0000",
"text": "The Sierpinski Gasket void displayQ glClear(GL_COLOR_BUFFER_BIT) ; g1Begin(GL_TRIANGLES) ; divide_triangle(v[o], v[1], v[2], n); glEndQ ; g1F1ushO 25 void myinitQ glMatrixMode(GL_PROJECTION); glloadIdentityQ; glu0rtho2D(-2.0, 2.0, -2.0, 2.0); g1MatrixMode(GL_MODELVIEW); glclearColor (1.0, 1.0, 1.0,1.0 glColor3f(0.0,0.0,0.0) ; } Faculty of Computer Science and Engineering - HCMUT Slide 7",
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"CO3059-chapter-3-slide-139-0000": {
"id": "CO3059-chapter-3-slide-139-0000",
"text": "The Sierpinski Gasket int **argv) main(int argc, char n=4 : glutInit(&argc, argv); glutInitDisplayMode(GLUT_SINGLEGLUT_RGB) ; glutInitWindowSize(500, 500); glutCreateWindow(\"2D Gasket\") ; glutDisplayFunc(display); myinitQ; glutMainLoopO ; r Faculty of Computer Science and Engineering - HCMUT Slide 8",
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"CO3059-chapter-3-slide-140-0000": {
"id": "CO3059-chapter-3-slide-140-0000",
"text": "The Sierpinski Gasket We can subdivide each of the four faces Appears as if we remove a solid tetrahedron from the center leaving four smaller tetrahedra Faculty of Computer Science and Engineering - HCMUT Slide 9",
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"CO3059-chapter-3-slide-141-0000": {
"id": "CO3059-chapter-3-slide-141-0000",
"text": "The Sierpinski Gasket *a1 GLfloat *c){ void triangle( GLfloat Glfloat *b, glVertex3fv(a) ; glVertex3fv(b) ; glVertex3fv(c) ; void tetra(GLfloat *a, GLfloat *b, GLfloat *c, GLfloat *d} glColor3fv(colors[0]) triangle(b, d, c); glColor3fv(colors[1]) triangle(a, b, c); glColor3fv(colors[2]) triangle(a, c, d); glColor3fv(colors[3]) triangle(a, d, b): Faculty of Computer Science and Engineering - HCMUT Slide 10",
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"text": "The Sierpinski Gasket void divide tetra(GLfloat *a, GLfloat *b, GLfloat *c, GLfloat *d, int m) GLfloat mid[6][3] int j; if(m>0) for(j=0;j<3;j++) mid[01j1=(a[j1+b[jD/2 divide tetra(a, mid[0], mid[1], mid[2], m-1 else(tetra(a,b,c,d)); /* draw tetrahedron at end of recursion */ Faculty of Computer Science and Engineering - HCMUT Slide 11",
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"text": "Hidden-Surface Removal Camera : (0, 0, 20) Teapot : (0, 0, -1) Sphere: (0, 0, 1) Cube: (0, 0, -3) Correct Order: CameraSphereTeapotCube Draw Order : TeapotSphere Cube Faculty of Computer Science and Engineering - HCMUT Slide 14",
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"text": "Hidden-Surface e Removal We want to see only those surfaces in front of other surfaces buffer algorithm that saves depth information as objects are rendered so that only the front objects appear in the image A B Faculty of Computer Science and Engineering - HCMUT Slide 17",
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"text": "Hidden-Surface e Removal store depth information as geometry travels down the pipeline It must be - Requested in main() glutInitDisplayMode(GLUT_SINGLE GLUT RGB GLUT I DEPTH) - Enabled glEnable(GL_DEPTH I_TEST) - Cleared in the display callback glClear(GL_COLOR BUFFER BIT GL DEPTH BUFFER BIT) Faculty of Computer Science and Engineering - HCMUT Slide 18",
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"text": "Modeling Sphere time frequency time frequency Faculty of Computer Science and Engineering - HCMUT Slide 20",
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"text": "Modeling Sphere Spherical coordinate system - x = r*sin(theta)*cos(phi): y - z = r*cos(theta)*cos(phi - y = r*sin(phi) M phi O x theta M' Z Faculty of Computer Science and Engineering - HCMUT Slide 21",
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"text": "Modeling Sphere l start start 3 2F 3v GL QUAD STRIP V4 V2 V6 Faculty of Computer Science and Engineering - HCMUT Slide 23",
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"text": "Modeling Sphere for(float phi = -80; phi<=80; phi+=20){ phir = c*phi; phir20 = c*(phi+20 glBegin(GL_QUAD_STRlP); for(float theta = -180; theta<=180; theta+=20) thetar = c*theta; x = sin(thetar)*cos(phir); z = cos(thetar)*cos(phir) y = sin(phir); glVertex3d(x, y, z); x = sin(thetar)*cos(phir20);z = cos(thetar)*cos(phir20); y = sin(phir20): gIVertex3d(x, y, z); gEndO Faculty of Computer Science and Engineering - HCMUT Slide 24",
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"text": "Modeling Sphere glBegin(GL_TRIANGLE_FAN); glVertex3d(0,1, 0) c80 = c*80; y = sin(c80) for(float theta = 180; theta>=-180; theta-=20) thetar = c*theta: x = sin(thetar)*cos(c80); z = cos(thetar)*cos(c80) glVertex3d(x,y, z); gEndO Faculty of Computer Science and Engineering - HCMUT Slide 25",
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"text": "Data Structure GLfIoat a[3]={ 0,0,0},b[3]={ 1,0,0} GLfloat c[3]={ 0,1,0},d[3]={ 0,0,1}; glPoygonMode(GL_FRONT_AND_BACK,GL_LINE): glBegin(GL_TRIANGLES); Y glVertex3fv(a);glVertex3fv(b);glVertex3fv(c); glVertex3fv(a); glVertex3fv(b); glVertex3fv(d C glVertex3fv(a); glVertex3fv(c); glVertex3fv(d) glVertex3fv(b); glVertex3fv(c); glVertex3fv(d gEndO a d b Z X Faculty of Computer Science and Engineering - HCMUT Slide 31",
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"text": "Data Structure struct Face int numVerts, Point3D *pointArr; }; class Mesh f int numFaces Face *faceArr; DrawWireframe0 : void void DrawColorO; }; Faculty of Computer r Science and Engineering - HCMUT Slide 32",
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"text": "Modeling Shapes with Polygonal Meshes Defining a Polygonal Mesh vertex list, a normal list, and a face list - The three lists work together : The vertex list contains locational or geometric information, the normal list contains orientation information, and the face list contains connectivity or topological information. Faculty of Computer Science and Engineering - HCMUT Slide 33",
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"text": "Modeling Shapes with Polygonal Meshes vertex x y y normal Ix 1y 12 I1 3 0 0 0 0 0 -1 4 1 1 0 0 8 0.707 0 2 I6 2 1 1 0 1 0.707 9 no 0.707 0.707 0 3 0.5 1.5 0 7 2 113 4 0 1 0 1 0 0 15 5 1 3 x 5 0 0 1 0 -1 0 6 6 1 0 1 4 4 0 0 14 1 7 1 1 1 5 8 0.5 1.5 1 0 0 -1 face vertices associated normal 6 9 0 1 0 (left) 0.5.9.4 0.0.0.0 1 (roof left) 3.4.9.8 1.1.1.1 2 (roof right) 2.3.8.7 2.2.2.2 3 (right) 1.2.7.6 3.3.3.3 4 (bottom) 0.1.6.5 4,4.4.4 5 (front) 5.6.7.8.9 5.5.5.5.5 6 (back) 0.4.3.2.1 6.6.6.6.6 Faculty of Computer Science and Engineering - HCMUT Slide 34",
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"text": "Modeling Shapes with Polygonal Meshes class VertexID{ public: int vertIndex; //index of this vertex in the vertex list int normlndex: // index of this vertex's normal }; class Face{ public: int nVerts; // number of vertice in this face VertexlD* vert: // the list of vertex and normal index FaceO{ nVerts = 0;vert = NULL;} FaceO { delete[] vert; nVerts = 0; } }; Faculty of Computer Science and Engineering - HCMUT Slide 35",
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"text": "Modeling Shapes with Polygonal Meshes class Mesh { private: int numVerts: / number of vertices in the mesh Point3* pt; // array of 3D vertices int numNormals; // number of normal vectors for the mesh Vector3* norm; // array of normals int numFaces; // number of faces in the mesh Face* face; // array of face data // ... others to be added later public: MeshO MeshO; //... others }; Faculty of Computer Science and Engineering - HCMUT Slide 36",
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"text": "Modeling Shapes with Polygonal Meshes void Mesh::DrawWireframeOt gIPolygonMode(GL_FRONT_AND_BACK,GL_LINE); for (int f = 0; f < numFaces; f++) { glBegin(GL_POLYGON); int iv = face[f].vert[v].vertlndex; glVertex3f(pt[iv].x, pt[iv].y, pt[iv].z); glEndO Faculty of Computer Science and Engineering - HCMUT Slide 37",
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"text": "Modeling Shapes with Polygonal Meshes a) b) 1 2 numVerts 4 1 pt 1 numNorms 4 .577 -1 .577 -1 norm 0 .577 -1 4 3 3 3 3 3 1 Z x 1 0 0 2 1 3 2 2 1 3 2 3 3 3 0 1 1 2 2 0 3 Faculty of Computer r Science and Engineering - HCMUT Slide 38",
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"text": "Modeling Shapes with Polygonal Meshes void Mesh::CreateTetrahedronO numVerts=4: pt = new Point3[numVerts]; pt[0].set(0, 0, 0); pt[1].set(1, 0, 0) pt[2].set(0, 1, 0) pt[3].set(0, 0, 1), Faculty of Computer Science and Engineering - HCMUT Slide 39",
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"text": "Modeling Shapes with Polygonal Meshes numFaces= 4; face = new Face[numFaces1; face[0].nVerts = 3; face[0].vert = new VertexlD[face[0].nVerts]; face[0].vert[0].vertlndex = 1; face[0].vert[1].vertlndex = 2; face[0].vert[2].vertlndex = 3; face[0].vert[0].normIndex = 0; face[0].vert[1].normlndex = 0; face[0].vert[2].normlndex = 0; Faculty of Computer Science and Engineering - HCMUT Slide 40",
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"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 04: Input & Interaction",
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"text": "Windows-based programming WPS PDF glut-3.spec.pdf X + 1 Sign in Menu B S 4 Home Insert Comment Edit Page Protect Tools Q Click to search : sW Hand Tool D 100% Fit Width Q 28 /68P Select Tool PDF to Word PDF to Picture Play Slide Zoom Out Zoom In Actual Size ] Fit Size Clockwise Anticlockwise Rotate Previous Bookmark x 7.4 glutKeyboardFunc glutKeyboardFunc scts the kcyboard callback for thc current window. 4 7Callback Registration Usage 7.1 glutDisplayFunc void glutKeyboardFunc(void (*func)(unsigned char key, 7.2 glutOverlayDisplayFunc int x, int y; 7.3 glutReshapeFunc 7.4 glutKeyboardFunc 7.5 glutMouseFunc 7.6 glutMotionFunc, glutPas... 7.7 glutVisibilityFunc 7.8 glutEntryFunc 22 7. CALLBACK REGISTRATION 7.9 glutSpecialFunc func The ncw keyboard callback function. 7.10 glutSpaceballMotionFunc Description 7.11 glutSpaceballRotateFunc glutKeyboardFunc sets the kcyboard callback for the current window. When a uscr types into the window 7.12 glutSpaceballButtonFunc cach key press generating an ASCIl character will gencrate a keyboard callback. The key callback parameter is the generated ASCIl character. The state of modificr keys such as Shift cannot be determined directly, thcir 7.13 glutButtonBoxFunc only cffect will be on the returmcd ASCll data.The x and y callback paramcters indicate the mouse location in window relative coordinates when the key was pressed.When a new window is created, no keyboard callback is 7.14 gutDiasFunc initiallyregistered,and ASCIl key strokes in the window are ignored. Passing NULL to glutKeyboardFunc disables the gencration of keyboard callbacks. 7.15 glutTabletMotionFunc During a kcyboard callback,glutGetModi f ier s may be called to determine the state of modificr kcys when the keystroke generating the callback occurred. 7.16 glutTabletButtonFunc Also,sce glutSpecialFunc for a mcans to detect non-ASCll kcy strokes 28 /68Page 80 0 1-1 100% Faculty of Computer Science and Engineering - HCMUT Slide 11",
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"text": "Reshape Event The reshape callback - glutReshapeFunc(myreshape); - void myReshape( int w, int h) Returns width and height of new window (in pixels) - A redisplay is posted automatically at end of execution of the callback - GLUT has a default reshape callback but you probably want to define your own - The reshape callback is good place to put viewing functions because it is invoked when the window is first opened Faculty of Computer Science and Engineering - HCMUT Slide 18",
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"text": "Reshape Event void myReshape(int w, int h){ float factor = 2; glViewport(0, 0, w, h) glMatrixMode(GL_PROJECTION) glLoadldentityO if (w <= h) glOrtho(-factor, factor, -factor * h / w, factor * h / w, -10.0, 10.0) else glOrtho(-factor * w / h, factor * w / h -factor, factor, -10.0, 10.0) Faculty of Computer Science and Engineering - HCMUT Slide 21",
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"text": "Reshape Event void myReshape(int w, int h){ float factor = 2; glViewport(0, 0, w, h): glMatrixMode(GL_PROJECTlON) glLoadldentityO if (w <= h) glOrtho(-factor, factor, -factor * h / w, factor * h / w, -10.0, 10.0): else glOrtho(-factor * w / h,factor * w / h -factor, factor, -10.0, 10.0): Faculty of Computer Science and Engineering - HCMUT Slide 23",
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"text": "Idle Event The idle callback is executed whenever there are no events in the event queue glutldleFunc(myidle) Useful for animations void myidle0 { /* change something */ t += dt glutPostRedisplayO void mydisplay0 t glClearO; /* draw something that depends on t */ glutSwapBuffersO: Faculty of Computer Science and Engineering - HCMUT Slide 24",
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"text": "Double Buffer Double Buffering - Instead of one color buffer, we use two Front Buffer: one that is displayed but not written to Back Buffer: one that is written to but not displayed - Program then requests a double buffer in main.c glutInitDisplayMode(GL_RGB GL DOUBLE) At the end of the display callback buffers are swapped void mydisplayO { glClear(GL COLOR BUFFER ? BIT[.... /* draw graphics here */ glutSwapBuffersO Faculty of Computer Science and Engineering - HCMUT Slide 25",
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"text": "Toolkits and Widgets Most window systems provide a toolkit or library of functions for building user interfaces that use special types of windows called widgets - Menus - Slidebars - Dials - Input boxes But toolkits tend to be platform dependent GLUT provides a few widgets including menus Faculty of Computer Science and Engineering - HCMUT Slide 26",
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"text": "Toolkits and Widgets Menu - Menu callback void mymenu(int id) { if(id == 1) glClear0; if(id == 2) exit(0); - Note each menu has an id that is returned when it is created by - Add submenus glutAddSubMenu(char *submenu_name, submenu id) Faculty of Computer Science and Engineering - HCMUT Slide 29",
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"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 05: Vector in Computer Graphics",
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"text": "OUTLINE Vector Dot product Cross Product Scalars Points Affine Sums Parametric Form D Line Plane Some Example F Representation Faculty of Computer r Science and Engineering - HCMUT Slide 2",
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"text": "Vector Why vector important? - Remove Hidden-face - Normal vector - Three basic elements in geometry: scalar, point. vector (4,6 tam ? (5.3) (2,2) mat phang nhin Faculty of Computer Science and Engineering - HCMUT Slide 3",
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"text": "Vector 1 I Physical definition: a vector is a quantity with two attributes: 1)Direction; 2)Magnitude Examples include: 1)Force; 2)Velocity - Same length and magnitude b) 4 P 3 Y P 2 1 2 3 4 x 1 x Z Faculty of Computer Science and Engineering - HCMUT Slide 4",
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"text": "Vector A=(1,2,9),B =(4,6,3 AB = (4 - 1, 6 - 2, 3 - 9) = (3, 4, -6) BA =(1- 4, 2 - 6, 9 - 3) = (-3, -4, 6) Faculty of Computer Science and Engineering - HCMUT Slide 5",
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"text": "Vector a =(2,5, 6),b =(-2,7,1) Addition: a + b = (0, 12, 7) Scalar-vector multiplication: 6a = (12, 30, 39) Subtraction: a - b = a + (-b) =(4, -2, 5) b a +b a +b a a Faculty of Computer Science and Engineering - HCMUT Slide 6",
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"text": "Vector a 2.5a -a a- c a- c a :1 c c c Faculty of Computer Science and Engineering - HCMUT Slide 7",
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"text": "Vector Magnitude: 2 2 w=Vw1 W +. .+ W n a Unit vector: u a a Faculty of Computer Science and Engineering - HCMUT Slide 8",
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"text": "Dot product and has the value: n V;W i=1 Properties - Symmetry: a-b = b-a - Linearity: (a + c)-b = a-b + c-b - Homogeneity: (sa)-b = s(a-b) -b2= b-b Faculty of Computer Science and Engineering - HCMUT Slide 9",
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"CO3059-chapter-5-slide-210-0000": {
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"text": "Dot product The angle between two vectors b*c =bc cos(0 cos(0) uc b b 6 c ho cI bo c= 0 boc=I Faculty of Computer r Science and Engineering - HCMUT Slide 10",
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"CO3059-chapter-5-slide-211-0000": {
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"text": "Dot product N=(A,B,C Vview Faculty of Computer Science and Engineering - HCMUT Slide 11",
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"text": "Dot product The 2D \"perp\"vector - Suppose a = (ax, ay), then a I = (-ay, ax) is the counterclockwise perpendicular to a. : a a :21 Faculty of Computer Science and Engineering - HCMUT Slide 12",
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"CO3059-chapter-5-slide-213-0000": {
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"text": "Dot product a line 1 FfT C F E + + c = Kv + Mvl (K,M=?) Faculty of Computer Science and Engineering - HCMUT Slide 13",
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"text": "Dot product c = Kv + Mv (K,M =?) (cx,cy) = K(vx,vy) + M(vx\",vy) cX = K*vx + M*vx\" cy = K*vy + M*vy Faculty of Computer Science and Engineering - HCMUT Slide 14",
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"CO3059-chapter-5-slide-215-0000": {
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"text": "Dot Product c = Kv + Mv (K,M =?) V c*v = Kvv + Mv1ov K = c*v1 = Kvov + Mv1ov1 M 0 v + distance = c = sl2 v Faculty of Computer Science and Engineering - HCMUT Slide 15",
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"CO3059-chapter-5-slide-216-0000": {
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"text": "Dot product Reflection r = e-m, e = a- m lr = a - 2m a o n =(a* u.)u m 2 n r = a - 2(a. un)u b) a) n n a a I m -m e1 62 1 e e Faculty of Computer r Science and Engineering - HCMUT Slide 16",
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"CO3059-chapter-5-slide-217-0000": {
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"text": "Cross Product cross product of a and b is a x b = (aybz-a,by)i + (a,bx- axbz)j + (axby - aybx)k 4 a x b 1 k 1 dien tich=a x b a Xb =a a a a x b b b x N b a X b =absin(0 Faculty of Computer Science and Engineering - HCMUT Slide 17",
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"text": "Parametric Form Explicit y = -x2 + 4x - 4 A3 0 1 2 3 A4 -3 A1 How to draw x2 + y2 = 1 Faculty of Computer Science and Engineering - HCMUT Slide 18",
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"text": "Parametric Form Parametric form - Ex 1: a straight line passes through A and B. Choose a parametric form that visit A at t = 0, visit B at t = 1. x(t) = Ax + (Bx - Ax)t y(t) = Ay + (By -Ay)t a t= 1 B (Bx, By) a t = 0 A (Ax, Ay) Faculty of Computer Science and Engineering - HCMUT Slide 19",
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"text": "Parametric Form Parametric form (x/W)2 + (y/H)2 = 1 Ellipse JDx y(t) EX 2: Ellipse with radius W and H t=/2 (x(t), H H x(t) = Wcos(t) y(t)) 2 t W y(t) = Hsin(t) -C c x t t=t H v6i ( 0<t <2t) -W W x(t) Tt 2t 1 Faculty of Computer r Science and Engineering - HCMUT Slide 20",
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"CO3059-chapter-5-slide-221-0000": {
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"text": "Parametric Form Draw parametric form curve a) t = T b) m P /t = 0 P(t) = (x(t), y(t)) //draw the curve (x(t), t(t)) using //the array t[0], ..., t[n-1] of \"sample-times glBegin(GL_LINE_STRIP) ; for(int i=0;i<n;i++) glvertex2f(x(t[i]), y(t[i])); glEndO ; Faculty of Computer r Science and Engineering - HCMUT Slide 21",
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"CO3059-chapter-5-slide-222-0000": {
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"text": "Parametric Form Superellipse - Implicit form Dx The SuperEllipse n n x y + =1 W H - Parametric form 2/n- x(t) =W cos(t)cos (t) 2/n-1 y(t) =H sin(t)sin (t) n = 2m/(2n+1) n < 1 inward n > 1 outward n = 1 sguare Faculty of Computer Science and Engineering - HCMUT Slide 22",
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"CO3059-chapter-5-slide-223-0000": {
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"text": "Parametric Form Superhyperbola - Parametric form The Superhyperbola x(t) =W sec(t)sec2 2/n- 2/n- y(t) =H tan(t)/tan (t) n = 2m/(2n+1) n < 1 inward n > 1 outward n = 1 line Faculty of Computer r Science and Engineering - HCMUT Slide 23",
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"text": "Parametric Form 3D curves The helix P(t) = (x(t), y(t), z(t)) Helix x(t) = cos(t) y(t) = sin(t) z(t) = bt The toroidal spiral Toroidal spiral x(t) = (asin(ct) + b)cos(t) y(t) = (asin(ct) + b)sin(t) z(t) = acos(ct) Faculty of Computer Science and Engineering - HCMUT Slide 24",
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"text": "Parametric Form x = cos(t) - cos(80*t)*sin(t): y = 2.0*sin(t) - sin(80*t); Plot parametric curves Faculty of Computer Science and Engineering - HCMUT Slide 25",
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"id": "CO3059-chapter-5-slide-226-0000",
"text": "Parametric Form x = cos(t); y = sin(t + sin(5.0*t)); Plot parametric curves Faculty of Computer Science and Engineering - HCMUT Slide 26",
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"text": "Parametric Form x = sin(t+sin(t)) y = cos(t + cos(t)); Plot parametric curves -0x Faculty of Computer Science and Engineering - HCMUT Slide 27",
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"text": "Parametric Form 2.0*sin(2.0*t); X = t + 2.0*c0s(5.0*t y = t + Plot parametric curves ox Faculty of Computer Science and Engineering - HCMUT Slide 28",
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"id": "CO3059-chapter-5-slide-229-0000",
"text": "Parametric Form x = t + sin(2.0*t): y = t + sin(3.0*t); Plot parametric curves Faculty of Computer Science and Engineering - HCMUT Slide 29",
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"id": "CO3059-chapter-5-slide-230-0000",
"text": "Parametric Form x = sin(3.0*t); y = sin(4.0*t) Plot parametric curves Faculty of Computer Science and Engineering - HCMUT Slide 30",
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"text": "Line (1) y = 5x + 3 (2) x = 1 x - 3 y + 2 2 - 3 (3) 1 6 -2 a) line b) line segment c) ray B B B C C C starting point Faculty of Computer Science and Engineering - HCMUT Slide 31",
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"text": "Line Line, line segment, ray a) line b) line segment c) ray B B B C C C starting point Parametric form y at L(t) = C + bt B Line segment, 0 t 1 1 b C Ray,0 t o @t = 1 @t = 0 Line, -o < t < o @t 0 x Faculty of Computer r Science and Engineering - HCMUT Slide 32",
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"CO3059-chapter-5-slide-233-0000": {
"id": "CO3059-chapter-5-slide-233-0000",
"text": "Line Point-normal form: n-(R - C) = 0 n B R Conversion B=C-n two- point {C,B point normal C,n} form form (2D only) n=(B-C) 11 + b b=B parametric form {C,b} Faculty of Computer Science and Engineering - HCMUT Slide 33",
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"CO3059-chapter-5-slide-234-0000": {
"id": "CO3059-chapter-5-slide-234-0000",
"text": "Plane Parametric form: P(s,t) = C + sa + tb C Point-normal form: n-(R - C) = 0 n= axb Faculty of Computer r Science and Engineering - HCMUT Slide 34",
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"CO3059-chapter-5-slide-235-0000": {
"id": "CO3059-chapter-5-slide-235-0000",
"text": "Plane Conversion A = (0,0,n· c/nz) B = (0, n· c/ny,0) three- point {C,B,A point normal C,n} form form n =(B-C) X(A- C) A =C + a B =C +b a=A-C b=B -C parametric form {C,a,b} Faculty of Computer Science and Engineering - HCMUT Slide 35",
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"CO3059-chapter-5-slide-236-0000": {
"id": "CO3059-chapter-5-slide-236-0000",
"text": "Some Examples Intersection of two line segment AB(t) =A + bt ; CD(u) = C + du Eind t and u such as A + bt = C + du bt= c+ du v6i c = C-A d-. bt= d-. c B B B a) b) c) D dob 7 O D D d-.c A t = A A C d-.b C D b-.c d) e D u = B B d-.b A C C A dob=0 Faculty of Computer Science and Engineering - HCMUT Slide 36",
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"CO3059-chapter-5-slide-237-0000": {
"id": "CO3059-chapter-5-slide-237-0000",
"text": "Some Examples The Circle throuah 3 points a) Which circle? b) What it looks like c) How to find its center A A A perpendicular ? ? bisector #2 S C C perpendicular c bisector #1 B B B 7 Perpendicular bisector L(t) =- (A+B)+(B- A)-t a=B -A; b=C -B;c=A - C; Perp. bisector AB: A + a/2 + a-t ; AC: A - c/2 + c-u a+t = b/2 + c-u 1 b.c 1 b. c S =A+- t = a + a 2a-.c 2 a C Faculty of Computer Science and Engineering - HCMUT Slide 37",
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"CO3059-chapter-5-slide-238-0000": {
"id": "CO3059-chapter-5-slide-238-0000",
"text": "Representation y t P b / V b a - - 0 1 X 0 X -- a v = a + b = 2.1i + 1.2j v = (2.1,1.2 P = O + OP = O + a + b = O + 3.9i + 3.7i P = (3.9,3.7) Faculty of Computer Science and Engineering - HCMUT Slide 38",
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"timestamp": "2025-10-31T22:33:06+07:00"
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"CO3059-chapter-5-slide-239-0000": {
"id": "CO3059-chapter-5-slide-239-0000",
"text": "Representation X x V P y y v = 1.6i + 2.7j v = (1.6, 2.7) P = (1.9,3.6) Faculty of Computer Science and Engineering - HCMUT Slide 39",
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"text": "Representation Frames - Frame determined by (P., v1, v,, v.) v=av+1,vzt - Every point can be written as P = P,+ bv+,v,+....+I.v. Faculty of Computer Science and Engineering - HCMUT Slide 40",
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"CO3059-chapter-5-slide-241-0000": {
"id": "CO3059-chapter-5-slide-241-0000",
"text": "Representation y 4 V P 0 X v = (2,1); P = (2, 1) Faculty of Computer Science and Engineering - HCMUT Slide 41",
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"CO3059-chapter-5-slide-242-0000": {
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"text": "Representation v = 2*i + 1*j = = 2*i + 1*j + 0*O V (2,1,0) P = 2*i+ 1*j + O P = 2*i+ 1*j+ 1*O (2,1,1) 0 X Faculty of Computer Science and Engineering - HCMUT Slide 42",
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"text": "Representation A Single Representation If we define 0-P = 0 and 1:P =P then we can write 1 V=OV1+ 0,V2 +azVz=[aAz Ag 0][v vz Vz P,] P=Po+ Bvs+ Bzvz+Bzvs=[B Bz Bz1][v Vzvz P] Thus we obtain the four-dimensional homogeneous coordinate representation v=[a&&0] p=[BBzBz1] 7 Faculty of Computer Science and Engineering - HCMUT Slide 43",
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"text": "Representation Homogeneous Coordinates The homogeneous coordinates form for a three dimensional point [x y z] is given as T p=[x'y'z'w]T=[wx wy wz w] We return to a three dimensional point (for w0) by xX'/w yy'/w z< z'/w If w=0, the representation is that of a vector Note that homogeneous coordinates replaces points in three dimensions by lines through the origin in four dimensions For w=1, the representation of a point is [x y z 1] Faculty of Computer Science and Engineering - HCMUT Slide 44",
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"CO3059-chapter-5-slide-245-0000": {
"id": "CO3059-chapter-5-slide-245-0000",
"text": "Representation with respect to two different bases. The representations are a=[a1 a2 2 Q3] b=[B1 Bz Bs] where Faculty of Computer Science and Engineering - HCMUT Slide 45",
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"text": "Representation - Each of the basis vectors, u1,u2, u3, are vectors that can be represented in terms of the first basis V U1= 91V1+I1zVz+1 V. 23 U3= I31V1+l3a 32V,+ V 32 33 3 Faculty of Computer Science and Engineering - HCMUT Slide 46",
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"text": "Representation The coefficients define a 3 x 3 matrix X11 X12 X13 X21 X22 X23 M = X31 X32 X33 and the bases can be related by a=Mtb Faculty of Computer Science and Engineering - HCMUT Slide 47",
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"CO3059-chapter-5-slide-248-0000": {
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"text": "Representation Change of Coordinate Systems 1 0 u2 V1 = ;V2 = 0 1 W v2 u1 =3v1 =2v2 u2 1 v1 u1 3 0 3 ;(m T 3 M = ;M 1 0 2 0 2 0 2] 1 1 0 1 3 3 :b =Ta = a = 1 1 1 1 2 2 Faculty of Computer r Science and Engineering - HCMUT Slide 48",
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"CO3059-chapter-5-slide-249-0000": {
"id": "CO3059-chapter-5-slide-249-0000",
"text": "Representation N W U1=V1+ V2 u2 =- V1+ V2 1 1 1 -1 T v2 M = ;M u2 u1 1 1 1 - 1 1 1 v1 (m1)1 2 2 1 1 - 1 1 1 1 2 2 a = - 2 2. 1 1 1 0 2 2. Faculty of Computer r Science and Engineering - HCMUT Slide 49",
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"text": "Representation Change of Frames - We can apply a similar process in homogeneous coordinates to the representations of both points and vectors u2 u1 Consider two frames: Qo (Po,V1,V2,V3) (Qo,u1,U2, uz) P 0 V U3 V 3 - Any point or vector can be represented in either frame Faculty of Computer Science and Engineering - HCMUT Slide 50",
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"CO3059-chapter-5-slide-251-0000": {
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"text": "Representation Change of Frames Extending what we did with change of bases uq= X1V+X12Vz+X13V3 Uz= Y21V1+X22Vz+X23V3 U3= X31V+X32Vz+Y33V3 Qo= X4iV+Y4Vz+Y 43V3+X44Po defining a 4 x 4 matrix 0 X11 X12 X13 X21 X22 X23 0 M = X31 X33 0 X32 X41 X42 X43 1 Faculty of Computer Science and Engineering - HCMUT Slide 51",
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"CO3059-chapter-5-slide-252-0000": {
"id": "CO3059-chapter-5-slide-252-0000",
"text": "Representation Change of Frames Within the two frames any point or vector has a representation of the same form a=[a g] in the first frame b=[B B BB]in the second frame where a=B= 1 for points and &=B= 0 for vectors and a=MTb The matrix M is 4 x 4 and specifies an affine transformation in homogeneous coordinates Faculty of Computer Science and Engineering - HCMUT Slide 52",
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"CO3059-chapter-6-slide-253-0000": {
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"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 06: Transformations",
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"CO3059-chapter-6-slide-254-0000": {
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"text": "OUTLINE Introduction Transformation in 2D Transformation in 3D Transformation in OpenGL Faculty of Computer Science and Engineering - HCMUT Slide 2",
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"text": "Introduction Introduction X @Introduction D X Introduction X @Introduction X Introduction D X glscalef(1.5, 0.5, 1); glTranslatef(1.5, 2.5, 0); glRotatef(30, 0, 0, 1; Faculty of Computer Science and Engineering - HCMUT Slide 3",
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"CO3059-chapter-6-slide-256-0000": {
"id": "CO3059-chapter-6-slide-256-0000",
"text": "Introduction General Transformations A transformation maps points to other points and/or vectors to other vectors v=T(u) P T Q=T(P) Faculty of Computer Science and Engineering - HCMUT Slide 4",
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"id": "CO3059-chapter-6-slide-257-0000",
"text": "Introduction General Transformations P = (Px,Py,1); Q =(Qx,Qy,1) (Q - image) (Qx,Qy,1) = T (Px,Py,1) (T - transformation) Q = T(P) a) b) V y T 0 P 0 P x x z Faculty of Computer Science and Engineering - HCMUT Slide 5",
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"CO3059-chapter-6-slide-258-0000": {
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"text": "Introduction General Transformations a) b) y after after before before x x Faculty of Computer r Science and Engineering - HCMUT Slide 6",
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"CO3059-chapter-6-slide-259-0000": {
"id": "CO3059-chapter-6-slide-259-0000",
"text": "Introduction Affine Transformations +m +m m X 11 X 121 y 13 Qy P +m P +m 21 22 23 X y m13 P x x m22 P m 23 y 1 0 0 1 1 always (0, 0,1) T Faculty of Computer r Science and Engineering - HCMUT Slide 7",
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"CO3059-chapter-6-slide-260-0000": {
"id": "CO3059-chapter-6-slide-260-0000",
"text": "Introduction Affine Transformations - Line preserving - Characteristic of many physically important transformations Rigid body transformations: rotation translation Scaling, shear - Importance in graphics is that we need only transform endpoints of line segments and let implementation draw line segment between the transformed endpoints Faculty of Computer Science and Engineering - HCMUT Slide 8",
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"text": "Introduction Pipeline Implementation glBegin(GL_LINES); glVertex3f(. : .); glVertex3f(. : .); glVertex3f(. : .); glEndO PyP Q1 Q CT y P 2 Z x x Z Faculty of Computer Science and Engineering - HCMUT Slide 9",
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"CO3059-chapter-6-slide-262-0000": {
"id": "CO3059-chapter-6-slide-262-0000",
"text": "Transformations in 2D Translation 0 m13 P Q 1 Qx = Px + m13 x x 0 1 m, P Qy = Py + m23 23 y 1 0 0 1 1 y 1 0 2 y 0 1 1 0 0 1 1 x x 2 Faculty of Computer r Science and Engineering - HCMUT Slide 10",
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"CO3059-chapter-6-slide-263-0000": {
"id": "CO3059-chapter-6-slide-263-0000",
"text": "Transformations in 2D Scaling S 0 0 P Q x x x Qx = Sx Px Q 0 S 0 P Qy = Sy Py y y y 1 0 0 1 1 1.3 0 0 uniform y 0 1.3 0 0 0 x 2 1.5 0 0 Non- x uniform 0 0.5 0 0 0 x Faculty of Computer r Science and Engineering - HCMUT Slide 11",
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"text": "Transformations in 2D Rotation cos(0) - sin(0) 0 Qx = Px cos(0) - Pv sin(0) sin(0) cos(0) X 0 sin(0) + P, cos(0) X 0 0 1 0.5 - V3/2 0 V3/2 0.5 0 t y 0 1 60o x x Faculty of Computer Science and Engineering - HCMUT Slide 14",
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"text": "Transformations in 2D Concatenation - We can form arbitrary affine transformation matrices by multiplying together rotation, translation, and scaling matrices - Because the same transformation is applied to many vertices, the cost of forming a matrix M=ABCD is not significant compared to the cost of computing Mp for many vertices p Faculty of Computer Science and Engineering - HCMUT Slide 18",
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"text": "Transformations in 2D Concatenation - Note that matrix on the right is the first applied - Mathematically, the following are equivalent W=TzQ= Tz(TP)=(TzT)P y T20 P W TO x Faculty of Computer Science and Engineering - HCMUT Slide 19",
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"text": "Transformations in 2D Concatenation - Move fixed point to origin - Rotate Q P V - Move fixed point back 0 P' - M = T(pi) R(0) T(-Pt) 1 0 V. cos(0) - sin(0) 0 1 0 -V x x 0 1 V sin(0) cos(0) 0 0 1 -V y y 0 0 1 0 0 1 0 0 1 cos(0) - sin(0) d x dx=-Vx cos(6)+V,sin(0)+V sin(0) cos(0) dy=-Vx sin(0)-Vy cos(0)+Vy d y 0 0 Faculty of Computer Science and Engineering - HCMUT Slide 20",
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"text": "Transformations in 3D General Formula m12 m13 m m21 m22 m24 M = m31 M32 M33 M34 0 0 0 1 Q P x x P =M y Q P. 1 1 Faculty of Computer Science and Engineering - HCMUT Slide 22",
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"text": "Transformations in 3D Translation 1 0 0 m. 0 1 0 0 0 1 0 0 1 Scaling V S 0 0 0 x 0 S y 0 0 S 0 Z x x 0 0 0 1 Faculty of Computer r Science and Engineering - HCMUT Slide 23",
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"text": "Transformations in 3D Shear 1 0 0 1 0 0 X V7 0 0 1 0 0 0 0 1 Rotation x-roll,y-roll, z-roll y when angle = 90°: P' Q' z-roll: xDy 0 x-roll: y0z P y-roll: z0x Z x Faculty of Computer Science and Engineering - HCMUT Slide 24",
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"text": "Transformations in 3D Rotation 1 0 0 0 0 0 s 0 0 c c - s 0 0 c - s 0 1 0 s 0 c R.(B) = R,(B)= R,(B) = 0 s 0 c 0 c 0 0 0 1 0 s 0 0 0 1 0 0 0 0 0 0 1 a) object b) Rotate about Ox c) Rotate about Oy d) Rotate aboute (- 70°) (30°) Oz (- 90°) y y y x Z x z x Z x z Faculty of Computer r Science and Engineering - HCMUT Slide 25",
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"text": "Transformations in 3D Rotation about an Arbitrary Axis u I x. Rotate about x axis with angle B Q B recover u. P 0 Z X Faculty of Computer Science and Engineering - HCMUT Slide 26",
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"text": "Transformations in 3D u X - Rotate u around y (+0) Q p - Then rotate around z (-) P Rotate around x (+B) Recover u 0 Z - Rotate around z (+o) x - Rotate around y (-0) Ru(B)=Ry(-0)Rz($)Rx(B)Rz(-$)Ry(0) Faculty of Computer r Science and Engineering - HCMUT Slide 27",
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"text": "Transformations in 3D y 1 Q B P Ru(B)=Rv(-0)Rz($)Rx(B)Rz(-$)Ry(0 0 x c+(1- c)ux (1- c)u,ux - su (1- c)u,u + su 0 (1- c)u.uy +su. c +(1- c)uy (1- c)u,uy - su 0 X (1- c)uzu, - su. (1- c)uyu, +su c+(1- c)u, 0 x 0 0 Faculty of Computer Science and Engineering - HCMUT Slide 28",
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"text": "Transformations in OpenGL How to draw this picture (the red letter H) float v0[12][2] = { {0, 0}, {0, 2}, {0.6, 2}, {0.6, 1.2}, {1.4, 1.2}, {1.4, 2}. {2, 2}, {2, 0}, {1.4, 0}, {1.4, 0.8}, {0.6, 0.8}, {0.6, 0} }; Transformation X void drawFigureoQ glColor3f(1, 0, 0); g1Begin(GL_LINE_LOOP); for (int i = 0; i < 12; i++) glVertex2fv(v0[i]); g1End); } Faculty of Computer Science and Engineering - HCMUT Slide 29",
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"text": "Transformations in OpenGL How to draw the blue H Transformation 0 4Y cos(60) sin(60) 0 cos(60) - sin(60) 4 0 1 5 sin(60) cos(60) 0 sin(60) cos(60) 5 0 0 0 0 0 0 1 Faculty of Computer Science and Engineering - HCMUT Slide 30",
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"text": "Transformations in OpenGL How to draw the blue H 0 4Ycos(60) sin(60) 0 cos(60) - sin(60) 4 0 1 5 sin(60) cos(60) 0 = sin(60) cos(60) 5S 0 0 0 0 0 0 1 void drawFigure1Q float v1[12][2]; for (int i = 0; i < 12; i++) v1[i][0] = v0[i][0] * cos(PI / 3) - v0[i][1] * sin(PI / 3) + 4; v1[i][1] = v0[i][0] * sin(PI / 3) + v0[i][1] * cos(PI / 3) + 5; } glColor3f(0, 0, 1); g1Begin(GL_LINE_LOOP); for (int i = 0; i < 12; i++ glVertex2fv(v1[i]); g1End(); Faculty of Computer Science and Engineering - HCMUT Slide 31",
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"text": "Transformations in OpenGL How to draw the purple H Transformation X cos(60) sin(60) 0 3 0 0 2 cos(60) 1 - 2 sin(60) 3 c0s(60) - 4 sin(60) sin(60) cos(60) 0 0 1 4 0 2 0 = 2 sin(60) 2 cos(60) 3sin(60)+ 4cos(60 0 0 0 0 0 0 0 0 1 Faculty of Computer Science and Engineering - HCMUT Slide 32",
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"text": "Transformations in OpenGL How to draw the purple H cos(60) - sin(60) 0 0 2 cos(60) - 2 sin(60) 3cos(60)- 4sin(60) sin(60) cos(60) 0 0 14 0 2 0 2 sin(60) 2 cos(60) 3sin(60)+ 4cos(60) 0 0 0 0 1 0 0 0 0 1 void drawFigure2Q{ float v2[12][2]; for (int i = 0; i < 12; i++){ v2[i][0] = v0[i][0] * 2*cos(PI / 3) - v0[i][1] * 2*sin(PI / 3) + 3*cos(PI/3)-4*sin(PI/3); v2[i][1] = v0[i][e] * 2*sin(PI / 3) + v0[i][1] * 2*cos(PI / 3) + 3*sin(PI/3)+4*cos(PI/3); } glColor3f(1, 0, 1); glBegin(GL_LINE_LOOP); for (int i = 0; i < 12; i++) glVertex2fv(v2[i]); g1End(); Faculty of Computer Science and Engineering - HCMUT Slide 33",
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"text": "Transformations in OpenGL How to draw the blue H Transformation X Faculty of Computer Science and Engineering - HCMUT Slide 34",
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"text": "Transformations in OpenGL void mydisplayQ f g1C1ear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_MODELVIEW)j glLoadIdentity(); drawGridQ; glColor3f(1, 0, 0);//The red H drawFigureeQ ; glColor3f(0, 0, 1); //The blue H glTranslatef(4, 5, 0); glRotatef(60, 0, 0, 1): drawFigure0(); glF1ushQ; } Faculty of Computer Science and Engineering - HCMUT Slide 35",
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"text": "Transformations in OpenGL glMatrixMode(GL_MODELVIEW) glLoadldentityO: CTM = I drawFigure0O CTM: Current Transf. Matrix S y Q S V S WV CTM V S Q Faculty of Computer r Science and Engineering - HCMUT Slide 36",
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"text": "Transformations in OpenGL glMatrixMode(GL_MODELVlEW); glLoadidentityO CTM = I 0 0 0 4 4 glColor3f(1,0, 0) 0 1 0 0 CTM = CTM* 1 0 0 1 0 0 0 1 0 drawFigure0O 0 0 0 1 0 0 0 1 glColor3f(0, 0, 1); cos(60) sin(60) 0 0 sin(60) cos(60) 0 0 glTranslatef(4, 5, 0); CTM = CTM* 0 0 1 0 glRotatef(60, 0, 0, 1); 0 0 0 1 drawFigure00; cos(60) sin(60) 0 4 sin(60) cos(60) 0 5 0 0 1 0 0 0 0 1 Faculty of Computer Science and Engineering - HCMUT Slide 37",
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"text": "Transformations in OpenGL glMatrixMode(GL_MODELVIEW); glLoadidentityO; Transformation X drawGridO glColor3f(0, 0, 1); glTranslatef(4, 5, 0)) glRotatef(60, 0, 0, 1); drawFigure00: glColor3f(1, 0, 0) drawFigure0O Faculty of Computer Science and Engineering - HCMUT Slide 38",
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"text": "Transformations in OpenGL glMatrixMode(GL_MODELVlEW); glLoadldentityO; CTM = l cos(60) - sin(60) 0 4 glColor3f(0, 0, 1); sin(60) cos(60) 0 5 glTranslatef(4, 5,0) CTM = 0 0 1 0 glRotatef(60,0,0,1); 0 0 0 1 drawFigure0O; glColor3f(1, 0, 0)) drawFigure0O Faculty of Computer Science and Engineering - HCMUT Slide 39",
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"text": "Transformations in OpenGL glMatrixMode(GL_MODELVlEW); glLoadidentityO; CTM = I glPushMatrixO; - glColor3f(0, 0,1);//The blue H cos(60) sin(60) 0 4 glTranslatef(4, 5, 0) CTM = sin(60) cos(60) 0 0 0 0 glRotatef(60, 0, 0, 1); 0 0 0 drawFigure0O: glPopMatrixO glColor3f(1, 0,0);//The red H CTM = I drawFigure0O Faculty of Computer Science and Engineering - HCMUT Slide 40",
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"text": "Transformations in OpenGL Tinh tién (M1) Truot theo truc y (M2 Ty Ié (M3) Tinh tién (M4) Faculty of Computer Science and Engineering - HCMUT Slide 55",
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"text": "Transformations in OpenGL 2D Transformation Q = m P +m P +m C B 11 12 13 X X y P +m P +m 21 22 y 23 x C -5 = m11 + m12 + m13 A D' 6 = m21 + m22 + m23 B 0 = 3m11+ 6m12 + m13 D 9 = 3m21 + 6m22 + m23 A 0 = 3m11 + 2m12 + m13 6 = 3m21 + 2m22 + m23 m11 = 5/2.m12 = 0, m13 = -15/2 m21 = -3/8, m22= 3/4,m23 = 45/8 Faculty of Computer Science and Engineering - HCMUT Slide 58",
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"text": "Transformations in OpenGL float Shear16l = f 1, -0.5, 0, 0, 0, 1, 0, 0. 0, 0, 1, 0. 0, 0, 0, 1}: float modelviewMatrix[16]; glColor3f(0, 0, 0; glPushMatrixO; glTranslatef(-5, 6, 0; glScalef(5 / 2.0, 3 / 4.0, 1); glMultMatrixf(Shear); glTranslatef(-1, -1, 0); glGetF1oatv(GL_MODELVIEW_MATRIX, modelviewMatrix)j printMatrix(modelviewMatrix); glPopMatrixQ; void printMatrix(float m[16]){ for (int i = 0; i < 4; i++){ printf(\"%8.4f %8.4f %8.4f %8.4f\", m[i], m[i + 4], m[i + 8], m[i + 12]; printf(\"n\"); Faculty of Computer Science and Engineering - HCMUT Slide 59",
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"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 7 : Viewing",
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"text": "OUTLINE Classical Viewing Orthographic Projection Axonometric Projections Oblique Projection Perspective Projection Computer Viewing View Volume Faculty of Computer Science and Engineering - HCMUT Slide 2",
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"text": "Classical Viewing MEND dreamstime.com ID127754469 LOCKA Download from ID 32507419 Dreamstime.com Richard ThomasDreamstime.com This watemmarked comp image is for previewine purpe sor Faculty of Computer Science and Engineering - HCMUT Slide 3",
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"text": "View Volume clip eye normalized window coordinates coordinates device coordinates coordinates VM P clip VqV2... modelview projection perspective viewport matrix matrix division matrix Perspective division: divide by w component (x,y, z,w) (x/w,y/w, z/w,1) Faculty of Computer Science and Engineering - HCMUT Slide 54",
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"text": "View volume Orthogonal projection - glortho(left, right,bottom, top,near,far) - near and far measured from camera right,top,-far View volume z=neor V (leff,bottom,-near n Faculty of Computer Science and Engineering - HCMUT Slide 55",
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"text": "Orthogonal Projection glortho(left,right,bottom, top,near,far) normalization =find transformation to convert specified clipping volume to default (right,top,-far) (1,1,-1 (left, bottom,-near -1,-1,1 Flip: -far 1; -near 1 O < near < far Faculty of Computer Science and Engineering - HCMUT Slide 56",
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"text": "Orthogonal Projection Two steps - Move center to origin T(-(left+right)/2, -(bottom+top)/2,(near+far)/2)) - Scale to have sides of length 2 S(2/(right-left),2/(top-bottom),2/(near-far)) 2 right + left 0 0 right - left right - left 2 top + bottom 0 0 P = ST = top - bottom top - bottom 2 far + near 0 0 near - far far - near 0 0 0 1 Faculty of Computer Science and Engineering - HCMUT Slide 57",
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"text": "Orthogonal Projection Set up projection matrix in the pipeline - Method 1 glMatrixMode(GL_PROJECTlON)j glLoadidentityO; gl0rtho(-1.2, 1.2, -1.2, 1.2, 0.1, 100); Faculty of Computer Science and Engineering - HCMUT Slide 58",
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"text": "Orthogonal Projection Set up projection matrix in the pipeline - Method 2 2 right + left 0 0 right - left right - left 2 top + bottom 0 0 top - bottom top - bottom 2 far + near 0 0 near- far far - near 0 0 0 1 float m[16] ..//Calculate m glMatrixMode(GL_PROJECTION); glLoadMatrixf(m); Faculty of Computer Science and Engineering - HCMUT Slide 59",
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"text": "Perspective Projection Perspective Projection - glFrustum(left, right,bottom,top,near,far) zeneor (right,topnear left,bottomnear V n Faculty of Computer Science and Engineering - HCMUT Slide 61",
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"text": "Perspective Projection Perspective Projection - With gIFrustum it is often difficult to get the desired view - gluPerpective(fovy, aspect, near, far) often provides a better interface W front plane aspect = w/h fov V n Faculty of Computer Science and Engineering - HCMUT Slide 62",
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"text": "Oblique Projections The OpenGL projection functions cannot produce general parallel projections such as appears that the cube has been sheared Faculty of Computer Science and Engineering - HCMUT Slide 64",
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"text": "Oblique Projections H P P orth n Faculty of Computer Science and Engineering - HCMUT Slide 65",
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"text": "Oblique Projections Back clipping plane Object Front clipping plane Projection plane DOP V n 69 (z, y) u 0) top view (O,Yp)) side view n n Faculty of Computer r Science and Engineering - HCMUT Slide 66",
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"text": "Oblique Projections Shear matrix xy shear (z values unchanged) 0 1 0 cot 0 0 1 cot 0 H(0,0) = 0 0 1 0 0 0 0 1 Projection matrix P = M H(0,) orth Faculty of Computer Science and Engineering - HCMUT Slide 67",
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"text": "Further Reading \"Interactive Computer Graphics: A Topdown Approach Using OpenGL\", Edward Ange/ - Chapter 5: Viewing \"D hoa máy tinh trong khng gian ba chiéu\", Tran Giang Son - Phép nhin trong khng gian ba chiéu Faculty of Computer Science and Engineering - HCMUT Slide 68",
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"CO3059-chapter-8-slide-380-0000": {
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"text": "Hochiminh city University of Technology Faculty of Computer Science and Engineering COMPUTER GRAPHICS CHAPTER 8: d Shading Lighting and",
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"text": "OUTLINE Introduction Shading model Flat shading & smooth shading Working with material in OpenGL Faculty of Computer Science and Engineering - HCMUT Slide 2",
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"text": "Introduction Wireframe - Simple, only edges of each object are drawn - Can see through object It can be difficult to see what's what Faculty of Computer Science and Engineering - HCMUT Slide 3",
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"text": "Introduction - Only edges are drawn - The objects now look solid, and it is easy to tell where one stops and the next begins Faculty of Computer Science and Engineering - HCMUT Slide 4",
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"text": "Introduction Flat shading - A calculation of how much light is scattered from each face is computed at a single point. - All points in a face are rendered with the same gray level - Can see the Boundary between polygons Faculty of Computer Science and Engineering - HCMUT Slide 5",
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"text": "Introduction Smooth shading (Gouraud shading) levels found through an interpolation scheme - The edges of polygons disappear specular Faculty of Computer Science and Engineering - HCMUT Slide 6",
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"text": "Introduction Adding texture, shadow Faculty of Computer Science and Engineering - HCMUT Slide 7",
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"text": "Introduction Before Projection After Projection Physical Model Mathematical Mode Faculty of Computer Science and Engineering - HCMUT Slide 8",
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"text": "Shading model objects, and the incident light interacts with the surface in three different ways: - Some is absorbed by the surface and is convert to heat - Some is reflected from the surface - Some is transmitted into the interior of the objects, as in the case of a piece of glass. Faculty of Computer Science and Engineering - HCMUT Slide 9",
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"text": "Shading model Two types of reflection of incident light: - Diffuse: re-radiated uniformly in all directions. Interacts strongly with the surface, so it color is usually affected by the nature of material. - Specular: highly directional, incident light doesnot penetrate the object, but instead is reflected directly from its outer surface. The reflected light has the same color as incident light. Faculty of Computer Science and Engineering - HCMUT Slide 10",
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"text": "Shading model Why does the imaae of a real teapot look like different color or shade To calculate color of the object, need to consider: - Light sources - Material properties - Location of viewer - Surface orientation Faculty of Computer Science and Engineering - HCMUT Slide 11",
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"text": "Shading model Geometric ingredients for finding reflected light - The normal vector m to the surface at P - The vector v from P to the viewer's eye - The vector s from P to the light source F Faculty of Computer Science and Engineering - HCMUT Slide 12",
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"text": "Shading model - Diffuse component with an intensity denoted by I. - Scattering uniform in all directions depend only on m,s S m Ia=IsPa m - Lambert's law: Iq =IsPa max 0 sm sm - I,: intensity of light source, P : diffuse reflection coefficient a) b) S m m e S S Faculty of Computer Science and Engineering - HCMUT Slide 13",
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"text": "Shading model Specular Reflection - Specular reflection causes highlights, which can add significantly to the realism of a picture when objects are shiny - The amount of light reflected is greated in the direction r. f m V r =- s + 2 =IsPs m 1 f : [1, 200] 2 sp m r v b) - m P Faculty of Computer Science and Engineering - HCMUT Slide 15",
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"text": "Shading model Specular Reflection - As f increase, the reflection becomes more mirror like and is more highly concentrated along the direction r. cos() 2 5 10 50 CL /2 Faculty of Computer Science and Engineering - HCMUT Slide 16",
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"text": "Shading model Combining Light Contribution h .m S .m lambert =max(0, and phong =max(0. hm sm Adding color + I Xlambert+ I Xphong 0 p dr dr ar ar spr sr 1 9 Xlambert + 1 Xphong * spg sg 1 Xlambert+ I ab P + p spb Psb Xphong ab db db Faculty of Computer Science and Engineering - HCMUT Slide 22",
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"text": "Introduction color1 x1,y1 X1.Y1.Z1 color1 X2,Y2,Z2 x2,y2 x3,y3 X3,Y3,Z3 color2 color2 color3 color3 Before Projection After Projection Physical Model Mathematical Model Faculty of Computer r Science and Engineering - HCMUT Slide 23",
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"text": "Flat shading & smooth shading Painting a face - The pixels in a polygon are visited in a regular order, usually scan line by scan line from bottom to top, and across each scan line from left to right - Convex polygons can be made highly efficient, since, at each scan line, there is a single unbroken 'run\" of pixels co1or3 for (int y = ybott ; y <= ytop ; y++) { Ytop find xleft and xright; color4 y4 for (int x = xleft; x <= xright; x++) { color2 ys find the color c for this pixel; y'bott color1 put c into the pixel at (x, y); } } Xleit Xriglt Faculty of Computer Science and Engineering - HCMUT Slide 24",
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"text": "Flat shading & smooth shading Flat shading - Face is flat, light source are quite distant diffuse light component varies little over different points - glShadeModel(GL_FLAT)) color3 Ytop for (int y = ybott ; y <= ytop ; y++) { color4 y4 find xleft and xright; color2 ys find the color c for this scan line; Ybott color1 for (int x = xleft; x <= xright; x++){ put c into the pixel at (x, y);}} Xleft Xrigkt Faculty of Computer Science and Engineering - HCMUT Slide 25",
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"text": "Flat shading & smooth shading Flat Shading x3,y3 (xleft - x4)/(xleft - x1) = co1or3 (cl - color4)/(cl-color1) Jtop x4, y4 co1or4 TT4 (xright - x2)/(xright - x1) x2,y2 color2 = (cr - color2)/(cr-color1) IE T bott. x1,y1 color1 Hleft Yrigt Faculty of Computer Science and Engineering - HCMUT Slide 26",
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"text": "Flat shading & smooth shading Smooth shading - Gouraud shading colorleft = lerp(color,, color4, f). Y4- Ybott X- X1eft color3 Ytop color4 y4 c(x+1) =c(x) + Xright color2 X1eft ys ybott color1 for (int y = ybott ; y <= ytop ; y++){ find xleft and xright; Xleit Xriglt find colorleft and colorright, colorinc = (colorright - colorleft)/ (xright - xleft) for (int x = xleft, c = colorleft; x <= xright; x++, c += colorinc ) { put c into the pixel at (x, y);}} Faculty of Computer Science and Engineering - HCMUT Slide 27",
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"text": "Steps in OpenGL shading -Enable shading and select model m -Specify normal -Specify lights -Specify material properties P 1 xlambert+1 phong 0 0 g ag ag spg sg pb Psb X phong h.m s.m m lambert=max(0 and phong = max(0 sm hm 8 Faculty of Computer Science and Engineering - HCMUT Slide 31",
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"text": "Enabling Shading Shading calculations are enabled by - glEnable(GL_LIGHTING) - Once lighting is enabled, glColorO ignored Must enable each light source individually - glEnable(GL_LIGHTi) i=0,1..... Faculty of Computer Science and Engineering - HCMUT Slide 32",
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"text": "Specify normals Set by glNormal*( - gINormal3f(x, y, z); - glNormal3fv(p); cosine calculations are correct - gEnable(GL_NORMALlZE) allows for autonormalization at a performance penalty Faculty of Computer Science and Engineering - HCMUT Slide 33",
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"text": "Using Light Sources in OpenGL Creating a light Source - Position GLfloat myLightPosition ={3.0, 6.0, 5.0, 1.0}; glLightfv(GL_LIGHT0,GL_POSITION,myLightPosition); (x, y, z, 1) point light source, (x, y, z, 0)directional light source - Color GLfloatamb0[ ={0.2, 0.4, 0.6, 1.0} GLfloatdiff0[] = {0.8, 0.9, 0.5, 1.0}; GLfloatspec0 ={1.0, 0.8, 1.0, 1.0} glLightfv(GL_LIGHT0,GL_AMBlENT, amb0)) glLightfv(GL_LIGHT0,GL_DIFFUSE,diff0) glLightfv(GL_LIGHT0,GL_SPECULAR,spec0 Faculty of Computer Science and Engineering - HCMUT Slide 34",
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"text": "Using Light Sources in OpenGL Creating a light source - Color GLfloat amb0[l ={0.2, 0.4, 0.6, 1.0} GLfloat diff0[] ={0.8, 0.9, 0.5, 1.0}; GLfloat spec0[] ={1.0, 0.8, 1.0, 1.0} glLightfv(GL_LIGHT0,GL_AMBIENT, amb0); gILightfv(GL_LIGHT0,GL_DIFFUSE,diff0): gILightfv(GL_LIGHT0, GL_SPECULAR,spec0); 1 xlambert+1 phongf - 1 0 g ag ag spg sg Ig=IabPab xlambert+ - Faculty of Computer r Science and Engineering - HCMUT Slide 35",
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"text": "Using Light Sources in OpenGL Splotlights glLightf(GL_LIGHT0,GL_SPOT_CUTOFF,45.0);// angle glLightf(GL_LIGHT0,GL_SPOT_EXPONENT,4.0);// c = 4.0 GLfloat dir[] = {2.0, 1.0, -4.0}; // direction glLightfv(GL_LIGHT0,GL_SPOT_DIRECTION,dir) d Faculty of Computer Science and Engineering - HCMUT Slide 36",
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"text": "Working with material in OpenGL GLfloat myColor[] ={0.8, 0.2, 0.0, 1.0}; gIMaterialfv(GL_FRONT, GL_DIFFUSE, myColor); GL BACK GL AMBIENT GL FRONT AND BACK GL SPECULAR,GL EMISSION spr Psr phong 1. xlambert+1 phong 1 0 ag ag g spg sg spb Psb phongf Faculty of Computer Science and Engineering - HCMUT Slide 37",
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"text": "Working with material in OpenGL GLfloat ambient[] = {0.2, 0.2, 0.2, 1.0}: GLfloat diffuse[] = {1.0, 0.8, 0.0, 1.0}; GLfloat specular[] = {1.0, 1.0, 1.0, 1.0}; GLfloat shine = 100.0 gIMaterialfv(GL_FRONT, GL_AMBlENT, ambient); gIMaterialfv(GL_FRONT, GL_DIFFUSE, diffuse), glMaterialfv(GL_FRONT, GL_SPECULAR, specular); gIMaterialf(GL_FRONT, GL_SHININESS, shine); .Ps. phong =1. phong' P 0 bo ag ag spg sg pbPsb phong Faculty of Computer Science and Engineering - HCMUT Slide 38",
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"text": "Front and Back Faces The default is shade only front faces which works correctly for convex objects sides of a surface Each side can have its own properties which are set by using GL_FRONT,GL_BACK,or GL FRONT AND BACK back faces not visible back faces visible Xem Video Clip: Chuo'ng 3 - Phän 7 Faculty of Computer Science and Engineering - HCMUT Slide 39",
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"text": "Computation of Vectors s and v are specified by the application Can compute r from s and m Problem is determining m determine m differs depending on underlying representation of surface OpenGL leaves determination of normal to application P Faculty of Computer Science and Engineering - HCMUT Slide 41",
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"text": "Computation of Vectors If the face is flat face's normal vector is vertices normal vector m = (V1 - V2) x (V3 - V4) Two problem: 1) two vector nearly parallel, 2) not all the vertices lie in the same plane N-1 m next( x i=0 - next() = (j + 1) mod N N-1 - Traversed in CCW m. i=0 - m outward N-1 i=0 Faculty of Computer Science and Engineering - HCMUT Slide 42",
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"text": "Computation of Vectors h A 112 n 3 4 8 2 06 no 9 7 0 15 1 x 6 V 1A 1 Faculty of Computer Science and Engineering - HCMUT Slide 43",
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"text": "Computation of Vectors Normal vector for a surface given parametrically 0p op n(uo,vo)= X Ou 0v u=Uo,V=Vc n(uo,vo) P(uo,vo) P(u,v) v-contoul u-contoul Faculty of Computer r Science and Engineering - HCMUT Slide 44",
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"text": "Computation of Vectors INormal vector for a surface given implicitly 0F OF OF n(xo,yo,z,)=VF x=Xo,y=Yo,z=Zo 0x 0z X=Xo,y=Yo,z=Zq EX: the implicit form of plane: F(x,y,z) = n. ((x,y,z) -A) = 0 or: nxx + ny+ nz -nA =0 normal is (nx, ny, n,) Faculty of Computer Science and Engineering - HCMUT Slide 45",
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"text": "Generic Shapes The sphere: normal (2x,2y,2z) al b) C) kinh tuyén x x x Z Z Z vi tuyén Faculty of Computer Science and Engineering - HCMUT Slide 46",
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"text": "Generic Shapes The sphere sin(v)) V dp/du = (-cos(v)sin(u),cos(v)cos(u), 0) V dp/dv = (-sin(v)cos(u),-sin(v)sin(u), cos(v)) V n(u,v) = (dp/du) x (dp/dv) = cos(v)p(u,v) 1 1 k a Xb =a a a X b b b x Z Faculty of Computer Science and Engineering - HCMUT Slide 47",
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"text": "Generic Shapes Cylinder: - Implicit form F(x,y, z) = x2 + y2 - (1 + (s - 1)z)2 0< z<1 n(x, y, z) = (x, y, -(s - 1)(1 + (s -1)z)) - Parametric form P(u, v) = ((1 + (s -1)v)cos(u), (1 + (s -1)v)sin(u), v) n(u, v) = (cos(u), sin(u), 1-s) a) b) y 1 1 (0,0,1) x x S Z Faculty of Computer Science and Engineering - HCMUT Slide 48",
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"text": "Generic Shape Cone Implicit: F(x,y,z) = x2 + y2 - (1 - z)2 = 0 0 < z < 1 n =(x,y,1 -z parametric P(u, v) = ((1 - v) cos(u), (1 - v)sin(u), v) n(u, v) = (cos(u), sin(u), 1) Faculty of Computer Science and Engineering - HCMUT Slide 49",
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"text": "Further Reading \"Interactive Computer Graphics: A Topdown Approach Using OpenGL\", Edward Ange/ - Chapter 6: Lighting and Shading \"D hoa máy tinh trong khng gian ba chiéu\", Tran Giang Son - Chuong 3: T mau vat thé ba chiéu (3.1 3.4) Faculty of Computer Science and Engineering - HCMUT Slide 50",
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