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'''
functions about rendering mesh(from 3d obj to 2d image).
only use rasterization render here.
Note that:
1. Generally, render func includes camera, light, raterize. Here no camera and light(I write these in other files)
2. Generally, the input vertices are normalized to [-1,1] and cetered on [0, 0]. (in world space)
Here, the vertices are using image coords, which centers on [w/2, h/2] with the y-axis pointing to oppisite direction.
Means: render here only conducts interpolation.(I just want to make the input flexible)
Preparation knowledge:
z-buffer: https://cs184.eecs.berkeley.edu/lecture/pipeline
Author: Yao Feng
Mail: yaofeng1995@gmail.com
'''
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from time import time
def isPointInTri(point, tri_points):
''' Judge whether the point is in the triangle
Method:
http://blackpawn.com/texts/pointinpoly/
Args:
point: (2,). [u, v] or [x, y]
tri_points: (3 vertices, 2 coords). three vertices(2d points) of a triangle.
Returns:
bool: true for in triangle
'''
tp = tri_points
# vectors
v0 = tp[2,:] - tp[0,:]
v1 = tp[1,:] - tp[0,:]
v2 = point - tp[0,:]
# dot products
dot00 = np.dot(v0.T, v0)
dot01 = np.dot(v0.T, v1)
dot02 = np.dot(v0.T, v2)
dot11 = np.dot(v1.T, v1)
dot12 = np.dot(v1.T, v2)
# barycentric coordinates
if dot00*dot11 - dot01*dot01 == 0:
inverDeno = 0
else:
inverDeno = 1/(dot00*dot11 - dot01*dot01)
u = (dot11*dot02 - dot01*dot12)*inverDeno
v = (dot00*dot12 - dot01*dot02)*inverDeno
# check if point in triangle
return (u >= 0) & (v >= 0) & (u + v < 1)
def get_point_weight(point, tri_points):
''' Get the weights of the position
Methods: https://gamedev.stackexchange.com/questions/23743/whats-the-most-efficient-way-to-find-barycentric-coordinates
-m1.compute the area of the triangles formed by embedding the point P inside the triangle
-m2.Christer Ericson's book "Real-Time Collision Detection". faster.(used)
Args:
point: (2,). [u, v] or [x, y]
tri_points: (3 vertices, 2 coords). three vertices(2d points) of a triangle.
Returns:
w0: weight of v0
w1: weight of v1
w2: weight of v3
'''
tp = tri_points
# vectors
v0 = tp[2,:] - tp[0,:]
v1 = tp[1,:] - tp[0,:]
v2 = point - tp[0,:]
# dot products
dot00 = np.dot(v0.T, v0)
dot01 = np.dot(v0.T, v1)
dot02 = np.dot(v0.T, v2)
dot11 = np.dot(v1.T, v1)
dot12 = np.dot(v1.T, v2)
# barycentric coordinates
if dot00*dot11 - dot01*dot01 == 0:
inverDeno = 0
else:
inverDeno = 1/(dot00*dot11 - dot01*dot01)
u = (dot11*dot02 - dot01*dot12)*inverDeno
v = (dot00*dot12 - dot01*dot02)*inverDeno
w0 = 1 - u - v
w1 = v
w2 = u
return w0, w1, w2
def rasterize_triangles(vertices, triangles, h, w):
'''
Args:
vertices: [nver, 3]
triangles: [ntri, 3]
h: height
w: width
Returns:
depth_buffer: [h, w] saves the depth, here, the bigger the z, the fronter the point.
triangle_buffer: [h, w] saves the tri id(-1 for no triangle).
barycentric_weight: [h, w, 3] saves corresponding barycentric weight.
# Each triangle has 3 vertices & Each vertex has 3 coordinates x, y, z.
# h, w is the size of rendering
'''
# initial
depth_buffer = np.zeros([h, w]) - 999999. #+ np.min(vertices[2,:]) - 999999. # set the initial z to the farest position
triangle_buffer = np.zeros([h, w], dtype = np.int32) - 1 # if tri id = -1, the pixel has no triangle correspondance
barycentric_weight = np.zeros([h, w, 3], dtype = np.float32) #
for i in range(triangles.shape[0]):
tri = triangles[i, :] # 3 vertex indices
# the inner bounding box
umin = max(int(np.ceil(np.min(vertices[tri, 0]))), 0)
umax = min(int(np.floor(np.max(vertices[tri, 0]))), w-1)
vmin = max(int(np.ceil(np.min(vertices[tri, 1]))), 0)
vmax = min(int(np.floor(np.max(vertices[tri, 1]))), h-1)
if umax<umin or vmax<vmin:
continue
for u in range(umin, umax+1):
for v in range(vmin, vmax+1):
if not isPointInTri([u,v], vertices[tri, :2]):
continue
w0, w1, w2 = get_point_weight([u, v], vertices[tri, :2]) # barycentric weight
point_depth = w0*vertices[tri[0], 2] + w1*vertices[tri[1], 2] + w2*vertices[tri[2], 2]
if point_depth > depth_buffer[v, u]:
depth_buffer[v, u] = point_depth
triangle_buffer[v, u] = i
barycentric_weight[v, u, :] = np.array([w0, w1, w2])
return depth_buffer, triangle_buffer, barycentric_weight
def render_colors_ras(vertices, triangles, colors, h, w, c = 3):
''' render mesh with colors(rasterize triangle first)
Args:
vertices: [nver, 3]
triangles: [ntri, 3]
colors: [nver, 3]
h: height
w: width
c: channel
Returns:
image: [h, w, c]. rendering.
'''
assert vertices.shape[0] == colors.shape[0]
depth_buffer, triangle_buffer, barycentric_weight = rasterize_triangles(vertices, triangles, h, w)
triangle_buffer_flat = np.reshape(triangle_buffer, [-1]) # [h*w]
barycentric_weight_flat = np.reshape(barycentric_weight, [-1, c]) #[h*w, c]
weight = barycentric_weight_flat[:, :, np.newaxis] # [h*w, 3(ver in tri), 1]
colors_flat = colors[triangles[triangle_buffer_flat, :], :] # [h*w(tri id in pixel), 3(ver in tri), c(color in ver)]
colors_flat = weight*colors_flat # [h*w, 3, 3]
colors_flat = np.sum(colors_flat, 1) #[h*w, 3]. add tri.
image = np.reshape(colors_flat, [h, w, c])
# mask = (triangle_buffer[:,:] > -1).astype(np.float32)
# image = image*mask[:,:,np.newaxis]
return image
def render_colors(vertices, triangles, colors, h, w, c = 3):
''' render mesh with colors
Args:
vertices: [nver, 3]
triangles: [ntri, 3]
colors: [nver, 3]
h: height
w: width
Returns:
image: [h, w, c].
'''
assert vertices.shape[0] == colors.shape[0]
# initial
image = np.zeros((h, w, c))
depth_buffer = np.zeros([h, w]) - 999999.
for i in range(triangles.shape[0]):
tri = triangles[i, :] # 3 vertex indices
# the inner bounding box
umin = max(int(np.ceil(np.min(vertices[tri, 0]))), 0)
umax = min(int(np.floor(np.max(vertices[tri, 0]))), w-1)
vmin = max(int(np.ceil(np.min(vertices[tri, 1]))), 0)
vmax = min(int(np.floor(np.max(vertices[tri, 1]))), h-1)
if umax<umin or vmax<vmin:
continue
for u in range(umin, umax+1):
for v in range(vmin, vmax+1):
if not isPointInTri([u,v], vertices[tri, :2]):
continue
w0, w1, w2 = get_point_weight([u, v], vertices[tri, :2])
point_depth = w0*vertices[tri[0], 2] + w1*vertices[tri[1], 2] + w2*vertices[tri[2], 2]
if point_depth > depth_buffer[v, u]:
depth_buffer[v, u] = point_depth
image[v, u, :] = w0*colors[tri[0], :] + w1*colors[tri[1], :] + w2*colors[tri[2], :]
return image
def render_texture(vertices, triangles, texture, tex_coords, tex_triangles, h, w, c = 3, mapping_type = 'nearest'):
''' render mesh with texture map
Args:
vertices: [nver], 3
triangles: [ntri, 3]
texture: [tex_h, tex_w, 3]
tex_coords: [ntexcoords, 3]
tex_triangles: [ntri, 3]
h: height of rendering
w: width of rendering
c: channel
mapping_type: 'bilinear' or 'nearest'
'''
assert triangles.shape[0] == tex_triangles.shape[0]
tex_h, tex_w, _ = texture.shape
# initial
image = np.zeros((h, w, c))
depth_buffer = np.zeros([h, w]) - 999999.
for i in range(triangles.shape[0]):
tri = triangles[i, :] # 3 vertex indices
tex_tri = tex_triangles[i, :] # 3 tex indice
# the inner bounding box
umin = max(int(np.ceil(np.min(vertices[tri, 0]))), 0)
umax = min(int(np.floor(np.max(vertices[tri, 0]))), w-1)
vmin = max(int(np.ceil(np.min(vertices[tri, 1]))), 0)
vmax = min(int(np.floor(np.max(vertices[tri, 1]))), h-1)
if umax<umin or vmax<vmin:
continue
for u in range(umin, umax+1):
for v in range(vmin, vmax+1):
if not isPointInTri([u,v], vertices[tri, :2]):
continue
w0, w1, w2 = get_point_weight([u, v], vertices[tri, :2])
point_depth = w0*vertices[tri[0], 2] + w1*vertices[tri[1], 2] + w2*vertices[tri[2], 2]
if point_depth > depth_buffer[v, u]:
# update depth
depth_buffer[v, u] = point_depth
# tex coord
tex_xy = w0*tex_coords[tex_tri[0], :] + w1*tex_coords[tex_tri[1], :] + w2*tex_coords[tex_tri[2], :]
tex_xy[0] = max(min(tex_xy[0], float(tex_w - 1)), 0.0);
tex_xy[1] = max(min(tex_xy[1], float(tex_h - 1)), 0.0);
# nearest
if mapping_type == 'nearest':
tex_xy = np.round(tex_xy).astype(np.int32)
tex_value = texture[tex_xy[1], tex_xy[0], :]
# bilinear
elif mapping_type == 'bilinear':
# next 4 pixels
ul = texture[int(np.floor(tex_xy[1])), int(np.floor(tex_xy[0])), :]
ur = texture[int(np.floor(tex_xy[1])), int(np.ceil(tex_xy[0])), :]
dl = texture[int(np.ceil(tex_xy[1])), int(np.floor(tex_xy[0])), :]
dr = texture[int(np.ceil(tex_xy[1])), int(np.ceil(tex_xy[0])), :]
yd = tex_xy[1] - np.floor(tex_xy[1])
xd = tex_xy[0] - np.floor(tex_xy[0])
tex_value = ul*(1-xd)*(1-yd) + ur*xd*(1-yd) + dl*(1-xd)*yd + dr*xd*yd
image[v, u, :] = tex_value
return image |