softgym/PyFlex/core/mesh.cpp

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#include "mesh.h"
#include "platform.h"

#include <map>
#include <fstream>
#include <iostream>

using namespace std;

void Mesh::DuplicateVertex(uint32_t i)
{
	assert(m_positions.size() > i);	
	m_positions.push_back(m_positions[i]);
	
	if (m_normals.size() > i)
		m_normals.push_back(m_normals[i]);
	
	if (m_colours.size() > i)
		m_colours.push_back(m_colours[i]);
	
	if (m_texcoords[0].size() > i)
		m_texcoords[0].push_back(m_texcoords[0][i]);
	
	if (m_texcoords[1].size() > i)
		m_texcoords[1].push_back(m_texcoords[1][i]);
	
}

void Mesh::Normalize(float s)
{
	Vec3 lower, upper;
	GetBounds(lower, upper);
	Vec3 edges = upper-lower;

	Transform(TranslationMatrix(Point3(-lower)));

	float maxEdge = max(edges.x, max(edges.y, edges.z));
	Transform(ScaleMatrix(s/maxEdge));
}

void Mesh::CalculateNormals()
{
	m_normals.resize(0);
	m_normals.resize(m_positions.size());

	int numTris = int(GetNumFaces());

	for (int i=0; i < numTris; ++i)
	{
		int a = m_indices[i*3+0];
		int b = m_indices[i*3+1];
		int c = m_indices[i*3+2];
		
		Vec3 n = Cross(m_positions[b]-m_positions[a], m_positions[c]-m_positions[a]);

		m_normals[a] += n;
		m_normals[b] += n;
		m_normals[c] += n;
	}

	int numVertices = int(GetNumVertices());

	for (int i=0; i < numVertices; ++i)
		m_normals[i] = ::Normalize(m_normals[i]);
}

namespace 
{

    enum PlyFormat
    {
        eAscii,
        eBinaryBigEndian    
    };

    template <typename T>
    T PlyRead(ifstream& s, PlyFormat format)
    {
        T data = eAscii;

        switch (format)
        {
            case eAscii:
            {
                s >> data;
                break;
            }
            case eBinaryBigEndian:
            {
                char c[sizeof(T)];
                s.read(c, sizeof(T));
                reverse(c, c+sizeof(T));
                data = *(T*)c;
                break;
            }      
			default:
				assert(0);
        }

        return data;
    }

} // namespace anonymous


Mesh* ImportMesh(const char* path)
{
	std::string ext = GetExtension(path);

	Mesh* mesh = NULL;

	if (ext == "ply")
		mesh = ImportMeshFromPly(path);
	else if (ext == "obj")
		mesh = ImportMeshFromObj(path);


	return mesh;
}

Mesh* ImportMeshFromBin(const char* path)
{
	double start = GetSeconds();

	FILE* f = fopen(path, "rb");

	if (f)
	{
		int numVertices;
		int numIndices;

		size_t len;
		len = fread(&numVertices, sizeof(numVertices), 1, f);
		len = fread(&numIndices, sizeof(numIndices), 1, f);

		Mesh* m = new Mesh();
		m->m_positions.resize(numVertices);
		m->m_normals.resize(numVertices);
		m->m_indices.resize(numIndices);

		len = fread(&m->m_positions[0], sizeof(Vec3)*numVertices, 1, f);
		len = fread(&m->m_normals[0], sizeof(Vec3)*numVertices, 1, f);
		len = fread(&m->m_indices[0], sizeof(int)*numIndices, 1, f);

		(void)len;
		
		fclose(f);

		double end = GetSeconds();

		printf("Imported mesh %s in %f ms\n", path, (end-start)*1000.0f);

		return m;
	}

	return NULL;
}

void ExportMeshToBin(const char* path, const Mesh* m)
{
	FILE* f = fopen(path, "wb");

	if (f)
	{
		int numVertices = int(m->m_positions.size());
		int numIndices = int(m->m_indices.size());

		fwrite(&numVertices, sizeof(numVertices), 1, f);
		fwrite(&numIndices, sizeof(numIndices), 1, f);

		// write data blocks
		fwrite(&m->m_positions[0], sizeof(Vec3)*numVertices, 1, f);
		fwrite(&m->m_normals[0], sizeof(Vec3)*numVertices, 1, f);		
		fwrite(&m->m_indices[0], sizeof(int)*numIndices, 1, f);

		fclose(f);
	}
}

Mesh* ImportMeshFromPly(const char* path)
{
    ifstream file(path, ios_base::in | ios_base::binary);

    if (!file)
        return NULL;

    // some scratch memory
    const uint32_t kMaxLineLength = 1024;
    char buffer[kMaxLineLength];

    //double startTime = GetSeconds();

    file >> buffer;
    if (strcmp(buffer, "ply") != 0)
        return NULL;

    PlyFormat format = eAscii;

    uint32_t numFaces = 0;
    uint32_t numVertices = 0;

    const uint32_t kMaxProperties = 16;
    uint32_t numProperties = 0; 
    float properties[kMaxProperties];

    bool vertexElement = false;

    while (file)
    {
        file >> buffer;

        if (strcmp(buffer, "element") == 0)
        {
            file >> buffer;

            if (strcmp(buffer, "face") == 0)
            {                
                vertexElement = false;
                file >> numFaces;
            }

            else if (strcmp(buffer, "vertex") == 0)
            {
                vertexElement = true;
                file >> numVertices;
            }
        }
        else if (strcmp(buffer, "format") == 0)
        {
            file >> buffer;
            if (strcmp(buffer, "ascii") == 0)
            {
                format = eAscii;
            }
            else if (strcmp(buffer, "binary_big_endian") == 0)
            {
                format = eBinaryBigEndian;
            }
			else
			{
				printf("Ply: unknown format\n");
				return NULL;
			}
        }
        else if (strcmp(buffer, "property") == 0)
        {
            if (vertexElement)
                ++numProperties;
        }
        else if (strcmp(buffer, "end_header") == 0)
        {
            break;
        }
    }

    // eat newline
    char nl;
    file.read(&nl, 1);
	
	// debug
#if ENABLE_VERBOSE_OUTPUT
	printf ("Loaded mesh: %s numFaces: %d numVertices: %d format: %d numProperties: %d\n", path, numFaces, numVertices, format, numProperties);
#endif

    Mesh* mesh = new Mesh;

    mesh->m_positions.resize(numVertices);
    mesh->m_normals.resize(numVertices);
    mesh->m_colours.resize(numVertices, Colour(1.0f, 1.0f, 1.0f, 1.0f));

    mesh->m_indices.reserve(numFaces*3);

    // read vertices
    for (uint32_t v=0; v < numVertices; ++v)
    {
        for (uint32_t i=0; i < numProperties; ++i)
        {
            properties[i] = PlyRead<float>(file, format);
        }

        mesh->m_positions[v] = Point3(properties[0], properties[1], properties[2]);
        mesh->m_normals[v] = Vector3(0.0f, 0.0f, 0.0f);
    }

    // read indices
    for (uint32_t f=0; f < numFaces; ++f)
    {
        uint32_t numIndices = (format == eAscii)?PlyRead<uint32_t>(file, format):PlyRead<uint8_t>(file, format);
		uint32_t indices[4];

		for (uint32_t i=0; i < numIndices; ++i)
		{
			indices[i] = PlyRead<uint32_t>(file, format);
		}

		switch (numIndices)
		{
		case 3:
			mesh->m_indices.push_back(indices[0]);
			mesh->m_indices.push_back(indices[1]);
			mesh->m_indices.push_back(indices[2]);
			break;
		case 4:
			mesh->m_indices.push_back(indices[0]);
			mesh->m_indices.push_back(indices[1]);
			mesh->m_indices.push_back(indices[2]);

			mesh->m_indices.push_back(indices[2]);
			mesh->m_indices.push_back(indices[3]);
			mesh->m_indices.push_back(indices[0]);
			break;

		default:
			assert(!"invalid number of indices, only support tris and quads");
			break;
		};

		// calculate vertex normals as we go
        Point3& v0 = mesh->m_positions[indices[0]];
        Point3& v1 = mesh->m_positions[indices[1]];
        Point3& v2 = mesh->m_positions[indices[2]];

        Vector3 n = SafeNormalize(Cross(v1-v0, v2-v0), Vector3(0.0f, 1.0f, 0.0f));

		for (uint32_t i=0; i < numIndices; ++i)
		{
	        mesh->m_normals[indices[i]] += n;
	    }
	}

    for (uint32_t i=0; i < numVertices; ++i)
    {
        mesh->m_normals[i] = SafeNormalize(mesh->m_normals[i], Vector3(0.0f, 1.0f, 0.0f));
    }

    //cout << "Imported mesh " << path << " in " << (GetSeconds()-startTime)*1000.f << "ms" << endl;

    return mesh;

}

// map of Material name to Material
struct VertexKey
{
	VertexKey() :  v(0), vt(0), vn(0) {}
	
	uint32_t v, vt, vn;
	
	bool operator == (const VertexKey& rhs) const
	{
		return v == rhs.v && vt == rhs.vt && vn == rhs.vn;
	}
	
	bool operator < (const VertexKey& rhs) const
	{
		if (v != rhs.v)
			return v < rhs.v;
		else if (vt != rhs.vt)
			return vt < rhs.vt;
		else
			return vn < rhs.vn;
	}
};

Mesh* ImportMeshFromObj(const char* path)
{
    ifstream file(path);

    if (!file)
        return NULL;

    Mesh* m = new Mesh();

    vector<Point3> positions;
    vector<Vector3> normals;
    vector<Vector2> texcoords;
    vector<Vector3> colors;
    vector<uint32_t>& indices = m->m_indices;

    //typedef unordered_map<VertexKey, uint32_t, MemoryHash<VertexKey> > VertexMap;
    typedef map<VertexKey, uint32_t> VertexMap;
    VertexMap vertexLookup;	

    // some scratch memory
    const uint32_t kMaxLineLength = 1024;
    char buffer[kMaxLineLength];

    //double startTime = GetSeconds();

    while (file)
    {
        file >> buffer;
	
        if (strcmp(buffer, "vn") == 0)
        {
            // normals
            float x, y, z;
            file >> x >> y >> z;

            normals.push_back(Vector3(x, y, z));
        }
        else if (strcmp(buffer, "vt") == 0)
        {
            // texture coords
            float u, v;
            file >> u >> v;

            texcoords.push_back(Vector2(u, v));
        }
        else if (buffer[0] == 'v')
        {
            // positions
            float x, y, z;
            file >> x >> y >> z;

            positions.push_back(Point3(x, y, z));
        }
        else if (buffer[0] == 's' || buffer[0] == 'g' || buffer[0] == 'o')
        {
            // ignore smoothing groups, groups and objects
            char linebuf[256];
            file.getline(linebuf, 256);		
        }
        else if (strcmp(buffer, "mtllib") == 0)
        {
            // ignored
            std::string MaterialFile;
            file >> MaterialFile;
        }		
        else if (strcmp(buffer, "usemtl") == 0)
        {
            // read Material name
            std::string materialName;
            file >> materialName;
        }
        else if (buffer[0] == 'f')
        {
            // faces
            uint32_t faceIndices[4];
            uint32_t faceIndexCount = 0;

            for (int i=0; i < 4; ++i)
            {
                VertexKey key;

                file >> key.v;

				if (!file.eof())
				{
					// failed to read another index continue on
					if (file.fail())
					{
						file.clear();
						break;
					}

					if (file.peek() == '/')
					{
						file.ignore();

						if (file.peek() != '/')
						{
							file >> key.vt;
						}

						if (file.peek() == '/')
						{
							file.ignore();
							file >> key.vn;
						}
					}

					// find / add vertex, index
					VertexMap::iterator iter = vertexLookup.find(key);

					if (iter != vertexLookup.end())
					{
						faceIndices[faceIndexCount++] = iter->second;
					}
					else
					{
						// add vertex
						uint32_t newIndex = uint32_t(m->m_positions.size());
						faceIndices[faceIndexCount++] = newIndex;

						vertexLookup.insert(make_pair(key, newIndex)); 	

						// push back vertex data
						assert(key.v > 0);

						m->m_positions.push_back(positions[key.v-1]);
						
						// obj format doesn't support mesh colours so add default value
						m->m_colours.push_back(Colour(1.0f, 1.0f, 1.0f));

						// normal [optional]
						if (key.vn)
						{
							m->m_normals.push_back(normals[key.vn-1]);
						}

						// texcoord [optional]
						if (key.vt)
						{
							m->m_texcoords[0].push_back(texcoords[key.vt-1]);
						}
					}
				}
            }

            if (faceIndexCount == 3)
            {
                // a triangle
                indices.insert(indices.end(), faceIndices, faceIndices+3);
            }
            else if (faceIndexCount == 4)
            {
                // a quad, triangulate clockwise
                indices.insert(indices.end(), faceIndices, faceIndices+3);

                indices.push_back(faceIndices[2]);
                indices.push_back(faceIndices[3]);
                indices.push_back(faceIndices[0]);
            }
            else
            {
                cout << "Face with more than 4 vertices are not supported" << endl;
            }

        }		
        else if (buffer[0] == '#')
        {
            // comment
            char linebuf[256];
            file.getline(linebuf, 256);
        }
    }

    // calculate normals if none specified in file
    m->m_normals.resize(m->m_positions.size());

    const uint32_t numFaces = uint32_t(indices.size())/3;
    for (uint32_t i=0; i < numFaces; ++i)
    {
        uint32_t a = indices[i*3+0];
        uint32_t b = indices[i*3+1];
        uint32_t c = indices[i*3+2];

        Point3& v0 = m->m_positions[a];
        Point3& v1 = m->m_positions[b];
        Point3& v2 = m->m_positions[c];

        Vector3 n = SafeNormalize(Cross(v1-v0, v2-v0), Vector3(0.0f, 1.0f, 0.0f));

        m->m_normals[a] += n;
        m->m_normals[b] += n;
        m->m_normals[c] += n;
    }

    for (uint32_t i=0; i < m->m_normals.size(); ++i)
    {
        m->m_normals[i] = SafeNormalize(m->m_normals[i], Vector3(0.0f, 1.0f, 0.0f));
    }
        
    //cout << "Imported mesh " << path << " in " << (GetSeconds()-startTime)*1000.f << "ms" << endl;

    return m;
}

void ExportToObj(const char* path, const Mesh& m)
{
	ofstream file(path);

    if (!file)
        return;

	file << "# positions" << endl;

	for (uint32_t i=0; i < m.m_positions.size(); ++i)
	{
		Point3 v = m.m_positions[i];
		file << "v " << v.x << " " << v.y << " " << v.z << endl;
	}

	file << "# texcoords" << endl;

	for (uint32_t i=0; i < m.m_texcoords[0].size(); ++i)
	{
		Vec2 t = m.m_texcoords[0][i];
		file << "vt " << t.x << " " << t.y << endl;
	}

	file << "# normals" << endl;

	for (uint32_t i=0; i < m.m_normals.size(); ++i)
	{
		Vec3 n = m.m_normals[0][i];
		file << "vn " << n.x << " " << n.y << " " << n.z << endl;
	}

	file << "# faces" << endl;

	for (uint32_t i=0; i < m.m_indices.size()/3; ++i)
	{
		uint32_t j = i+1;

		// no sharing, assumes there is a unique position, texcoord and normal for each vertex
		file << "f " << j << "/" << j << "/" << j << endl;
	}
}

void Mesh::AddMesh(const Mesh& m)
{
    uint32_t offset = uint32_t(m_positions.size());

    // add new vertices
    m_positions.insert(m_positions.end(), m.m_positions.begin(), m.m_positions.end());
    m_normals.insert(m_normals.end(), m.m_normals.begin(), m.m_normals.end());
    m_colours.insert(m_colours.end(), m.m_colours.begin(), m.m_colours.end());

    // add new indices with offset
    for (uint32_t i=0; i < m.m_indices.size(); ++i)
    {
        m_indices.push_back(m.m_indices[i]+offset);
    }    
}

void Mesh::Transform(const Matrix44& m)
{
    for (uint32_t i=0; i < m_positions.size(); ++i)
    {
        m_positions[i] = m*m_positions[i];
        m_normals[i] = m*m_normals[i];
    }
}

void Mesh::GetBounds(Vector3& outMinExtents, Vector3& outMaxExtents) const
{
    Point3 minExtents(FLT_MAX);
    Point3 maxExtents(-FLT_MAX);

    // calculate face bounds
    for (uint32_t i=0; i < m_positions.size(); ++i)
    {
        const Point3& a = m_positions[i];

        minExtents = Min(a, minExtents);
        maxExtents = Max(a, maxExtents);
    }

    outMinExtents = Vector3(minExtents);
    outMaxExtents = Vector3(maxExtents);
}

Mesh* CreateTriMesh(float size, float y)
{
	uint32_t indices[] = { 0, 1, 2 };
	Point3 positions[3];
	Vector3 normals[3];

	positions[0] = Point3(-size, y, size);
	positions[1] = Point3(size, y, size);
	positions[2] = Point3(size, y, -size);

	normals[0] = Vector3(0.0f, 1.0f, 0.0f);
	normals[1] = Vector3(0.0f, 1.0f, 0.0f);
	normals[2] = Vector3(0.0f, 1.0f, 0.0f);

	Mesh* m = new Mesh();
	m->m_indices.insert(m->m_indices.begin(), indices, indices + 3);
	m->m_positions.insert(m->m_positions.begin(), positions, positions + 3);
	m->m_normals.insert(m->m_normals.begin(), normals, normals + 3);

	return m;
}

Mesh* CreateCubeMesh()
{
	const Point3 vertices[24] = 
	{
		Point3(0.5, 0.5, 0.5), 
		Point3(-0.5, 0.5, 0.5), 
		Point3(0.5, -0.5, 0.5), 
		Point3(-0.5, -0.5, 0.5), 
		Point3(0.5, 0.5, -0.5), 
		Point3(-0.5, 0.5, -0.5), 
		Point3(0.5, -0.5, -0.5), 
		Point3(-0.5, -0.5, -0.5), 
		Point3(0.5, 0.5, 0.5), 
		Point3(0.5, -0.5, 0.5), 
		Point3(0.5, 0.5, 0.5), 
		Point3(0.5, 0.5, -0.5), 
		Point3(-0.5, 0.5, 0.5), 
		Point3(-0.5, 0.5, -0.5), 
		Point3(0.5, -0.5, -0.5), 
		Point3(0.5, 0.5, -0.5), 
		Point3(-0.5, -0.5, -0.5), 
		Point3(0.5, -0.5, -0.5), 
		Point3(-0.5, -0.5, 0.5), 
		Point3(0.5, -0.5, 0.5), 
		Point3(-0.5, -0.5, -0.5), 
		Point3(-0.5, -0.5, 0.5), 
		Point3(-0.5, 0.5, -0.5), 
		Point3(-0.5, 0.5, 0.5)
	};

	const Vec3 normals[24] =
	{
		Vec3(0.0f, 0.0f, 1.0f), 
		Vec3(0.0f, 0.0f, 1.0f), 
		Vec3(0.0f, 0.0f, 1.0f), 
		Vec3(0.0f, 0.0f, 1.0f), 
		Vec3(1.0f, 0.0f, 0.0f), 
		Vec3(0.0f, 1.0f, 0.0f), 
		Vec3(1.0f, 0.0f, 0.0f), 
		Vec3(0.0f, 0.0f, -1.0f), 
		Vec3(1.0f, 0.0f, 0.0f), 
		Vec3(1.0f, 0.0f, 0.0f), 
		Vec3(0.0f, 1.0f, 0.0f), 
		Vec3(0.0f, 1.0f, 0.0f), 
		Vec3(0.0f, 1.0f, 0.0f), 
		Vec3(0.0f, 0.0f, -1.0f), 
		Vec3(0.0f, 0.0f, -1.0f), 
		Vec3(-0.0f, -0.0f, -1.0f), 
		Vec3(0.0f, -1.0f, 0.0f), 
		Vec3(0.0f, -1.0f, 0.0f), 
		Vec3(0.0f, -1.0f, 0.0f), 
		Vec3(-0.0f, -1.0f, -0.0f), 
		Vec3(-1.0f, 0.0f, 0.0f), 
		Vec3(-1.0f, 0.0f, 0.0f), 
		Vec3(-1.0f, 0.0f, 0.0f), 
		Vec3(-1.0f, -0.0f, -0.0f) 
	};	

	const int indices[36] = 
	{
		0, 1, 2,
		3, 2, 1, 
		8, 9, 4, 
		6, 4, 9, 
		10, 11, 12, 
		5, 12, 11, 
		7, 13, 14, 
		15, 14, 13, 
		16, 17, 18, 
		19, 18, 17, 
		20, 21, 22, 
		23, 22, 21
	};

	Mesh* m = new Mesh();
	m->m_positions.assign(vertices, vertices+24);
	m->m_normals.assign(normals, normals+24);
	m->m_indices.assign(indices, indices+36);

	return m;

}

Mesh* CreateQuadMesh(float size, float y)
{
    uint32_t indices[] = { 0, 1, 2, 2, 3, 0 };
    Point3 positions[4];
    Vector3 normals[4];

    positions[0] = Point3(-size, y, size);
    positions[1] = Point3(size, y, size);
    positions[2] = Point3(size, y, -size);
    positions[3] = Point3(-size, y, -size);
    
    normals[0] = Vector3(0.0f, 1.0f, 0.0f);
    normals[1] = Vector3(0.0f, 1.0f, 0.0f);
    normals[2] = Vector3(0.0f, 1.0f, 0.0f);
    normals[3] = Vector3(0.0f, 1.0f, 0.0f);

    Mesh* m = new Mesh();
    m->m_indices.insert(m->m_indices.begin(), indices, indices+6);
    m->m_positions.insert(m->m_positions.begin(), positions, positions+4);
    m->m_normals.insert(m->m_normals.begin(), normals, normals+4);

    return m;
}

Mesh* CreateDiscMesh(float radius, uint32_t segments)
{
	const uint32_t numVerts = 1 + segments;

	Mesh* m = new Mesh();
	m->m_positions.resize(numVerts);
	m->m_normals.resize(numVerts, Vec3(0.0f, 1.0f, 0.0f));

	m->m_positions[0] = Point3(0.0f);
	m->m_positions[1] = Point3(0.0f, 0.0f, radius);

	for (uint32_t i=1; i <= segments; ++i)
	{
		uint32_t nextVert = (i+1)%numVerts;

		if (nextVert == 0)
			nextVert = 1;
		
		m->m_positions[nextVert] = Point3(radius*Sin((float(i)/segments)*k2Pi), 0.0f, radius*Cos((float(i)/segments)*k2Pi));

		m->m_indices.push_back(0);
		m->m_indices.push_back(i);
		m->m_indices.push_back(nextVert);		
	}
	
	return m;
}

Mesh* CreateTetrahedron(float ground, float height)
{
	Mesh* m = new Mesh();

	const float dimValue = 1.0f / sqrtf(2.0f);
	const Point3 vertices[4] =
	{
		Point3(-1.0f, ground, -dimValue),
		Point3(1.0f, ground, -dimValue),
		Point3(0.0f, ground + height, dimValue),
		Point3(0.0f, ground, dimValue)
	};

	const int indices[12] = 
	{
		//winding order is counter-clockwise
		0, 2, 1,
		2, 3, 1,
		2, 0, 3,
		3, 0, 1
	};

	m->m_positions.assign(vertices, vertices+4);
	m->m_indices.assign(indices, indices+12);

	m->CalculateNormals();

	return m;
}


Mesh* CreateSphere(int slices, int segments, float radius)
{
	float dTheta = kPi / slices;
	float dPhi = k2Pi / segments;

	int vertsPerRow = segments + 1;

	Mesh* mesh = new Mesh();

	for (int i = 0; i <= slices; ++i)
	{
		float theta = dTheta*i;

		for (int j = 0; j <= segments; ++j)
		{
			float phi = dPhi*j;

			float x = sinf(theta)*cosf(phi);
			float y = cosf(theta);
			float z = sinf(theta)*sinf(phi);

			mesh->m_positions.push_back(Point3(x, y, z)*radius);
			mesh->m_normals.push_back(Vec3(x, y, z));

			if (i > 0 && j > 0)
			{
				int a = i*vertsPerRow + j;
				int b = (i - 1)*vertsPerRow + j;
				int c = (i - 1)*vertsPerRow + j - 1;
				int d = i*vertsPerRow + j - 1;

				// add a quad for this slice
				mesh->m_indices.push_back(b);
				mesh->m_indices.push_back(a);
				mesh->m_indices.push_back(d);

				mesh->m_indices.push_back(b);
				mesh->m_indices.push_back(d);
				mesh->m_indices.push_back(c);
			}
		}
	}

	return mesh;
}

Mesh* CreateCapsule(int slices, int segments, float radius, float halfHeight)
{
	float dTheta = kPi / (slices * 2);
	float dPhi = k2Pi / segments;

	int vertsPerRow = segments + 1;

	Mesh* mesh = new Mesh();

	float theta = 0.0f;

	for (int i = 0; i <= 2 * slices + 1; ++i)
	{
		for (int j = 0; j <= segments; ++j)
		{
			float phi = dPhi*j;

			float x = sinf(theta)*cosf(phi);
			float y = cosf(theta);
			float z = sinf(theta)*sinf(phi);

			// add y offset based on which hemisphere we're in
			float yoffset = (i < slices) ? halfHeight : -halfHeight;

			mesh->m_positions.push_back(Point3(x, y, z)*radius + Vec3(0.0f, yoffset, 0.0f));
			mesh->m_normals.push_back(Vec3(x, y, z));

			if (i > 0 && j > 0)
			{
				int a = i*vertsPerRow + j;
				int b = (i - 1)*vertsPerRow + j;
				int c = (i - 1)*vertsPerRow + j - 1;
				int d = i*vertsPerRow + j - 1;

				// add a quad for this slice
				mesh->m_indices.push_back(b);
				mesh->m_indices.push_back(a);
				mesh->m_indices.push_back(d);

				mesh->m_indices.push_back(b);
				mesh->m_indices.push_back(d);
				mesh->m_indices.push_back(c);
			}
		}

		// don't update theta for the middle slice
		if (i != slices)
			theta += dTheta;
	}

	return mesh;
}