void MeshMassPropertiesTests::testClosedTetrahedronMesh() {
// given a tetrahedron as a closed mesh of four tiangles
// verify MeshMassProperties computes the right nubers
// these numbers from the Tonon paper:
VectorOfPoints points;
points.push_back(btVector3(8.33220f, -11.86875f, 0.93355f));
points.push_back(btVector3(0.75523f, 5.00000f, 16.37072f));
points.push_back(btVector3(52.61236f, 5.00000f, -5.38580f));
points.push_back(btVector3(2.00000f, 5.00000f, 3.00000f));
btScalar expectedVolume = 1873.233236f;
btMatrix3x3 expectedInertia;
expectedInertia[0][0] = 43520.33257f;
expectedInertia[1][1] = 194711.28938f;
expectedInertia[2][2] = 191168.76173f;
expectedInertia[1][2] = -4417.66150f;
expectedInertia[2][1] = -4417.66150f;
expectedInertia[0][2] = 46343.16662f;
expectedInertia[2][0] = 46343.16662f;
expectedInertia[0][1] = -11996.20119f;
expectedInertia[1][0] = -11996.20119f;
btVector3 expectedCenterOfMass = 0.25f * (points[0] + points[1] + points[2] + points[3]);
VectorOfIndices triangles;
pushTriangle(triangles, 0, 2, 1);
pushTriangle(triangles, 0, 3, 2);
pushTriangle(triangles, 0, 1, 3);
pushTriangle(triangles, 1, 2, 3);
// compute mass properties
MeshMassProperties mesh(points, triangles);
// verify
QCOMPARE_WITH_ABS_ERROR(mesh._volume, expectedVolume, acceptableRelativeError * expectedVolume);
QCOMPARE_WITH_ABS_ERROR(mesh._centerOfMass, expectedCenterOfMass, acceptableAbsoluteError);
QCOMPARE_WITH_RELATIVE_ERROR(mesh._inertia, expectedInertia, acceptableRelativeError);
// test again, but this time shift the points so that the origin is definitely OUTSIDE the mesh
btVector3 shift = points[0] + expectedCenterOfMass;
for (int i = 0; i < (int)points.size(); ++i) {
points[i] += shift;
}
expectedCenterOfMass = 0.25f * (points[0] + points[1] + points[2] + points[3]);
// compute mass properties
mesh.computeMassProperties(points, triangles);
// verify
// QCOMPARE_WITH_ABS_ERROR(mesh._volume, expectedVolume, acceptableRelativeError * expectedVolume);
// QCOMPARE_WITH_ABS_ERROR(mesh._centerOfMass, expectedCenterOfMass, acceptableAbsoluteError);
// QCOMPARE_WITH_RELATIVE_ERROR(mesh._inertia, expectedInertia, acceptableRelativeError);
}
void sierpinskiGasket(unsigned int a, unsigned int b, unsigned int c, unsigned int level) {
if(level == 0) {
// Generate new vertices and call this function recursively
// ... insert your code here ...
pushTriangle(a, b, c);
// ... end of your code ...
}
else{
Vertex newTrianglePointA = Vertex((vertices[a].position.x+vertices[b].position.x)/2,
(vertices[a].position.y+vertices[b].position.y)/2);
Vertex newTrianglePointB = Vertex((vertices[b].position.x+vertices[c].position.x)/2,
(vertices[b].position.y+vertices[c].position.y)/2);
Vertex newTrianglePointC = Vertex((vertices[c].position.x+vertices[a].position.x)/2,
(vertices[c].position.y+vertices[a].position.y)/2);
int indexA = vertices.size();
int indexB = indexA+1;
int indexC = indexB+1;
vertices.push_back(newTrianglePointA);
vertices.push_back(newTrianglePointB);
vertices.push_back(newTrianglePointC);
level = level-1;
sierpinskiGasket(a, indexA, indexC, level);
sierpinskiGasket(indexA, b, indexB, level);
sierpinskiGasket(indexC, indexB, c, level);
}
}
Terrain::Terrain(int width, int height, int patchSize)
: m_width(width),
m_height(height),
m_patchSize(patchSize),
m_patchCount(width / patchSize, height / patchSize),
m_patchMesh(),
m_currentHeightMap(0),
m_shader()
{
for (int i = 0; i < 2; ++i)
{
m_heightMaps[i] = new FrameBuffer(width, height);
m_heightMaps[i]->edit();
m_heightMaps[i]->addColorTexture(GL_R32F);
m_heightMaps[i]->done();
}
std::vector<glm::vec3> vertices;
std::vector<unsigned short> indicies;
#define INDEX(x, z) ((z) * patchSize) + (x)
for (int z = 0; z < patchSize; ++z)
for (int x = 0; x < patchSize; ++x)
{
float ux = x / (patchSize - 1.0);
float uz = z / (patchSize - 1.0);
vertices.push_back(glm::vec3(ux, 0.0, uz));
if (z < (patchSize - 1) && x < (patchSize - 1))
{
pushTriangle(indicies, INDEX(x, z), INDEX(x, z + 1), INDEX(x + 1, z));
pushTriangle(indicies, INDEX(x, z + 1), INDEX(x + 1, z + 1), INDEX(x + 1, z));
}
}
m_patchMesh.addBuffer(Mesh::VERTEX, vertices);
m_patchMesh.addBuffer(Mesh::INDICIES, indicies);
m_patchMesh.setIndexCount(indicies.size());
m_shader.load("../../example/data/Terrain.vert", GL_VERTEX_SHADER);
m_shader.load("../../example/data/Terrain.frag", GL_FRAGMENT_SHADER);
m_shader.setupMeshAttributes();
m_shader.link();
}
void Rasterizer::pushTriangle(CanvasPortion *canvas, const Vector3 &v1, const Vector3 &v2, const Vector3 &v3) {
Vector3 p1, p2, p3;
p1 = getRenderer()->projectPoint(v1);
p2 = getRenderer()->projectPoint(v2);
p3 = getRenderer()->projectPoint(v3);
if (pushProjectedTriangle(canvas, p1, p2, p3, v1, v2, v3)) {
// Cutting needed
Vector3 vm1 = v1.midPointTo(v2);
Vector3 vm2 = v2.midPointTo(v3);
Vector3 vm3 = v3.midPointTo(v1);
pushTriangle(canvas, v1, vm1, vm3);
pushTriangle(canvas, v2, vm1, vm2);
pushTriangle(canvas, v3, vm3, vm2);
pushTriangle(canvas, vm1, vm2, vm3);
}
}
void MeshMassPropertiesTests::testOpenTetrahedonMesh() {
// given the simplest possible mesh (open, with one triangle)
// verify MeshMassProperties computes the right nubers
// these numbers from the Tonon paper:
VectorOfPoints points;
points.push_back(btVector3(8.33220f, -11.86875f, 0.93355f));
points.push_back(btVector3(0.75523f, 5.00000f, 16.37072f));
points.push_back(btVector3(52.61236f, 5.00000f, -5.38580f));
points.push_back(btVector3(2.00000f, 5.00000f, 3.00000f));
btScalar expectedVolume = 1873.233236f;
btMatrix3x3 expectedInertia;
expectedInertia[0][0] = 43520.33257f;
expectedInertia[1][1] = 194711.28938f;
expectedInertia[2][2] = 191168.76173f;
expectedInertia[1][2] = -4417.66150f;
expectedInertia[2][1] = -4417.66150f;
expectedInertia[0][2] = 46343.16662f;
expectedInertia[2][0] = 46343.16662f;
expectedInertia[0][1] = -11996.20119f;
expectedInertia[1][0] = -11996.20119f;
// test as an open mesh with one triangle
VectorOfPoints shiftedPoints;
shiftedPoints.push_back(points[0] - points[0]);
shiftedPoints.push_back(points[1] - points[0]);
shiftedPoints.push_back(points[2] - points[0]);
shiftedPoints.push_back(points[3] - points[0]);
VectorOfIndices triangles;
pushTriangle(triangles, 1, 2, 3);
btVector3 expectedCenterOfMass = 0.25f * (shiftedPoints[0] + shiftedPoints[1] + shiftedPoints[2] + shiftedPoints[3]);
// compute mass properties
MeshMassProperties mesh(shiftedPoints, triangles);
// verify
// (expected - actual) / expected > e ==> expected - actual > e * expected
QCOMPARE_WITH_ABS_ERROR(mesh._volume, expectedVolume, acceptableRelativeError * expectedVolume);
QCOMPARE_WITH_ABS_ERROR(mesh._centerOfMass, expectedCenterOfMass, acceptableAbsoluteError);
QCOMPARE_WITH_RELATIVE_ERROR(mesh._inertia, expectedInertia, acceptableRelativeError);
}
void SoCapsule::build ( float len, float rt, float rb, int nfaces )
{
P.clear(); C.clear(); // set size to zero, just in case
float hlen = len/2.0f;
int levels = std::ceil(static_cast<float>(nfaces) / 2.0f);
float faceAngularHeight = (static_cast<float>(M_PI) / 2.0) / static_cast<float>(levels);
float faceAngularLength = (2.0 * static_cast<float>(M_PI)) / static_cast<float>(nfaces);
int vertices = 2 + (2*levels + 1)*(nfaces * 6);
// Reserve space for the capsule vertices
P.reserve(vertices);
C.reserve(vertices);
// Generate the coordinates for the capsule body
std::vector<GsVec> bodyTopCoordinates;
std::vector<GsVec> bodyBottomCoordinates;
bodyTopCoordinates.reserve(nfaces);
bodyBottomCoordinates.reserve(nfaces);
// Compute the tube section of the capsule
for(int i = 0; i < nfaces; i++)
{
float p = static_cast<float>(i) * faceAngularLength;
bodyTopCoordinates.push_back(GsVec(rt * std::cos(p), hlen, rt * std::sin(p)));
bodyBottomCoordinates.push_back(GsVec(rb * std::cos(p), -hlen, rb * std::sin(p)));
}
pushLevel(P, C, bodyTopCoordinates, bodyBottomCoordinates, nfaces);
// Compute the top of the capsule
std::vector<GsVec>& previousTopVector = bodyTopCoordinates;
std::vector<GsVec> currentTopVector;
currentTopVector.reserve(nfaces);
for(int j = 1; j < levels; j++)
{
// theta coordinate
float t = static_cast<float>(j) * faceAngularHeight;
for(int i = 0; i < nfaces; i++)
{
// phi coordinate
float p = static_cast<float>(i) * faceAngularLength;
currentTopVector.push_back(GsVec((rt * std::cos(p)) * std::cos(t),
hlen + (rt * std::sin(t)),
(rt * std::sin(p)) * std::cos(t)));
}
pushLevel(P, C, currentTopVector, previousTopVector, nfaces);
std::swap(currentTopVector, previousTopVector);
currentTopVector.clear();
}
// Compute the cap of the capsule
GsVec tv(0.0f, hlen + rt, 0.0f);
for(int i = 0; i < nfaces; i++)
{
GsVec a = previousTopVector[i];
GsVec b = (i+1 == nfaces) ? previousTopVector[0] : previousTopVector[i+1];
pushTriangle(P, C, {a, b, tv});
}
// Compute the bottom of the capsule
std::vector<GsVec>& previousBottomVector = bodyBottomCoordinates;
std::vector<GsVec> currentBottomVector;
currentBottomVector.reserve(nfaces);
for(int j = 1; j < levels; j++)
{
// theta coordinate
float t = static_cast<float>(j) * faceAngularHeight;
for(int i = 0; i < nfaces; i++)
{
// phi coordinate
float p = static_cast<float>(i) * faceAngularLength;
currentBottomVector.push_back(GsVec((rb * std::cos(p)) * std::cos(t),
-hlen - (rb * std::sin(t)),
(rb * std::sin(p)) * std::cos(t)));
}
pushLevel(P, C, currentBottomVector, previousBottomVector, nfaces);
std::swap(currentBottomVector, previousBottomVector);
currentBottomVector.clear();
}
// Compute the cap of the capsule
GsVec bv(0.0f, -hlen - rb, 0.0f);
for(int i = 0; i < nfaces; i++)
{
GsVec a = previousBottomVector[i];
GsVec b = (i+1 == nfaces) ? previousBottomVector[0] : previousBottomVector[i+1];
pushTriangle(P, C, {a, bv, b});
}
//pushCap(P, C, previousBottomVector, bv, nfaces);
// send data to OpenGL buffers:
glBindBuffer ( GL_ARRAY_BUFFER, buf[0] );
glBufferData ( GL_ARRAY_BUFFER, P.size()*3*sizeof(float), &P[0], GL_STATIC_DRAW );
glBindBuffer ( GL_ARRAY_BUFFER, buf[1] );
glBufferData ( GL_ARRAY_BUFFER, C.size()*4*sizeof(gsbyte), &C[0], GL_STATIC_DRAW );
// save size so that we can free our buffers and later just draw the OpenGL arrays:
_numpoints = P.size();
// free non-needed memory:
P.resize(0); C.resize(0);
changed = 0;
}
void Rasterizer::pushQuad(CanvasPortion *canvas, const Vector3 &v1, const Vector3 &v2, const Vector3 &v3,
const Vector3 &v4) {
pushTriangle(canvas, v2, v3, v1);
pushTriangle(canvas, v4, v1, v3);
}
void MeshMassPropertiesTests::testBoxAsMesh() {
// verify that a mesh box produces the same mass properties as the analytic box.
// build a box:
// /
// y
// /
// 6-------------------------7
// /| /|
// / | / |
// / 2----------------------/--3
// / / / /
// | 4-------------------------5 / --x--
// z | / | /
// | |/ |/
// 0 ------------------------1
btScalar x(5.0f);
btScalar y(3.0f);
btScalar z(2.0f);
VectorOfPoints points;
points.reserve(8);
points.push_back(btVector3(0.0f, 0.0f, 0.0f));
points.push_back(btVector3(x, 0.0f, 0.0f));
points.push_back(btVector3(0.0f, y, 0.0f));
points.push_back(btVector3(x, y, 0.0f));
points.push_back(btVector3(0.0f, 0.0f, z));
points.push_back(btVector3(x, 0.0f, z));
points.push_back(btVector3(0.0f, y, z));
points.push_back(btVector3(x, y, z));
VectorOfIndices triangles;
pushTriangle(triangles, 0, 1, 4);
pushTriangle(triangles, 1, 5, 4);
pushTriangle(triangles, 1, 3, 5);
pushTriangle(triangles, 3, 7, 5);
pushTriangle(triangles, 2, 0, 6);
pushTriangle(triangles, 0, 4, 6);
pushTriangle(triangles, 3, 2, 7);
pushTriangle(triangles, 2, 6, 7);
pushTriangle(triangles, 4, 5, 6);
pushTriangle(triangles, 5, 7, 6);
pushTriangle(triangles, 0, 2, 1);
pushTriangle(triangles, 2, 3, 1);
// compute expected mass properties analytically
btVector3 expectedCenterOfMass = 0.5f * btVector3(x, y, z);
btScalar expectedVolume = x * y * z;
btMatrix3x3 expectedInertia;
computeBoxInertia(expectedVolume, btVector3(x, y, z), expectedInertia);
// compute the mass properties using the mesh
MeshMassProperties mesh(points, triangles);
// verify
QCOMPARE_WITH_ABS_ERROR(mesh._volume, expectedVolume, acceptableRelativeError * expectedVolume);
QCOMPARE_WITH_ABS_ERROR(mesh._centerOfMass, expectedCenterOfMass, acceptableAbsoluteError);
// test this twice: _RELATIVE_ERROR doesn't test zero cases (to avoid divide-by-zero); _ABS_ERROR does.
QCOMPARE_WITH_ABS_ERROR(mesh._inertia, expectedInertia, acceptableAbsoluteError);
QCOMPARE_WITH_RELATIVE_ERROR(mesh._inertia, expectedInertia, acceptableRelativeError);
// These two macros impl this:
// for (int i = 0; i < 3; ++i) {
// for (int j = 0; j < 3; ++j) {
// if (expectedInertia [i][j] == btScalar(0.0f)) {
// error = mesh._inertia[i][j] - expectedInertia[i][j]; // COMPARE_WITH_ABS_ERROR
// if (fabsf(error) > acceptableAbsoluteError) {
// std::cout << __FILE__ << ":" << __LINE__ << " ERROR : inertia[" << i << "][" << j << "] off by "
// << error << " absolute"<< std::endl;
// }
// } else {
// error = (mesh._inertia[i][j] - expectedInertia[i][j]) / expectedInertia[i][j]; // COMPARE_WITH_RELATIVE_ERROR
// if (fabsf(error) > acceptableRelativeError) {
// std::cout << __FILE__ << ":" << __LINE__ << " ERROR : inertia[" << i << "][" << j << "] off by "
// << error << std::endl;
// }
// }
// }
// }
}
