//--------------------------------------------------------------------------------------
// Torus
//--------------------------------------------------------------------------------------
void DirectX::ComputeTorus(VertexCollection& vertices, IndexCollection& indices, float diameter, float thickness, size_t tessellation, bool rhcoords)
{
vertices.clear();
indices.clear();
if (tessellation < 3)
throw std::out_of_range("tesselation parameter out of range");
size_t stride = tessellation + 1;
// First we loop around the main ring of the torus.
for (size_t i = 0; i <= tessellation; i++)
{
float u = float(i) / tessellation;
float outerAngle = i * XM_2PI / tessellation - XM_PIDIV2;
// Create a transform matrix that will align geometry to
// slice perpendicularly though the current ring position.
XMMATRIX transform = XMMatrixTranslation(diameter / 2, 0, 0) * XMMatrixRotationY(outerAngle);
// Now we loop along the other axis, around the side of the tube.
for (size_t j = 0; j <= tessellation; j++)
{
float v = 1 - float(j) / tessellation;
float innerAngle = j * XM_2PI / tessellation + XM_PI;
float dx, dy;
XMScalarSinCos(&dy, &dx, innerAngle);
// Create a vertex.
XMVECTOR normal = XMVectorSet(dx, dy, 0, 0);
XMVECTOR position = XMVectorScale(normal, thickness / 2);
XMVECTOR textureCoordinate = XMVectorSet(u, v, 0, 0);
position = XMVector3Transform(position, transform);
normal = XMVector3TransformNormal(normal, transform);
vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinate));
// And create indices for two triangles.
size_t nextI = (i + 1) % stride;
size_t nextJ = (j + 1) % stride;
index_push_back(indices, i * stride + j);
index_push_back(indices, i * stride + nextJ);
index_push_back(indices, nextI * stride + j);
index_push_back(indices, i * stride + nextJ);
index_push_back(indices, nextI * stride + nextJ);
index_push_back(indices, nextI * stride + j);
}
}
// Build RH above
if (!rhcoords)
ReverseWinding(indices, vertices);
}
//--------------------------------------------------------------------------------------
// Tetrahedron
//--------------------------------------------------------------------------------------
void DirectX::ComputeTetrahedron(VertexCollection& vertices, IndexCollection& indices, float size, bool rhcoords)
{
vertices.clear();
indices.clear();
static const XMVECTORF32 verts[4] =
{
{ { { 0.f, 0.f, 1.f, 0 } } },
{ { { 2.f*SQRT2 / 3.f, 0.f, -1.f / 3.f, 0 } } },
{ { { -SQRT2 / 3.f, SQRT6 / 3.f, -1.f / 3.f, 0 } } },
{ { { -SQRT2 / 3.f, -SQRT6 / 3.f, -1.f / 3.f, 0 } } }
};
static const uint32_t faces[4 * 3] =
{
0, 1, 2,
0, 2, 3,
0, 3, 1,
1, 3, 2,
};
for (size_t j = 0; j < _countof(faces); j += 3)
{
uint32_t v0 = faces[j];
uint32_t v1 = faces[j + 1];
uint32_t v2 = faces[j + 2];
XMVECTOR normal = XMVector3Cross(
XMVectorSubtract(verts[v1].v, verts[v0].v),
XMVectorSubtract(verts[v2].v, verts[v0].v));
normal = XMVector3Normalize(normal);
size_t base = vertices.size();
index_push_back(indices, base);
index_push_back(indices, base + 1);
index_push_back(indices, base + 2);
// Duplicate vertices to use face normals
XMVECTOR position = XMVectorScale(verts[v0], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, g_XMZero /* 0, 0 */));
position = XMVectorScale(verts[v1], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, g_XMIdentityR0 /* 1, 0 */));
position = XMVectorScale(verts[v2], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, g_XMIdentityR1 /* 0, 1 */));
}
// Built LH above
if (rhcoords)
ReverseWinding(indices, vertices);
assert(vertices.size() == 4 * 3);
assert(indices.size() == 4 * 3);
}
// Creates a cone primitive.
void DirectX::ComputeCone(VertexCollection& vertices, IndexCollection& indices, float diameter, float height, size_t tessellation, bool rhcoords)
{
vertices.clear();
indices.clear();
if (tessellation < 3)
throw std::out_of_range("tesselation parameter out of range");
height /= 2;
XMVECTOR topOffset = XMVectorScale(g_XMIdentityR1, height);
float radius = diameter / 2;
size_t stride = tessellation + 1;
// Create a ring of triangles around the outside of the cone.
for (size_t i = 0; i <= tessellation; i++)
{
XMVECTOR circlevec = GetCircleVector(i, tessellation);
XMVECTOR sideOffset = XMVectorScale(circlevec, radius);
float u = float(i) / tessellation;
XMVECTOR textureCoordinate = XMLoadFloat(&u);
XMVECTOR pt = XMVectorSubtract(sideOffset, topOffset);
XMVECTOR normal = XMVector3Cross(
GetCircleTangent(i, tessellation),
XMVectorSubtract(topOffset, pt));
normal = XMVector3Normalize(normal);
// Duplicate the top vertex for distinct normals
vertices.push_back(VertexPositionNormalTexture(topOffset, normal, g_XMZero));
vertices.push_back(VertexPositionNormalTexture(pt, normal, XMVectorAdd(textureCoordinate, g_XMIdentityR1)));
index_push_back(indices, i * 2);
index_push_back(indices, (i * 2 + 3) % (stride * 2));
index_push_back(indices, (i * 2 + 1) % (stride * 2));
}
// Create flat triangle fan caps to seal the bottom.
CreateCylinderCap(vertices, indices, tessellation, height, radius, false);
// Build RH above
if (!rhcoords)
ReverseWinding(indices, vertices);
}
// Creates a teapot primitive.
void DirectX::ComputeTeapot(VertexCollection& vertices, IndexCollection& indices, float size, size_t tessellation, bool rhcoords)
{
vertices.clear();
indices.clear();
if (tessellation < 1)
throw std::out_of_range("tesselation parameter out of range");
XMVECTOR scaleVector = XMVectorReplicate(size);
XMVECTOR scaleNegateX = XMVectorMultiply(scaleVector, g_XMNegateX);
XMVECTOR scaleNegateZ = XMVectorMultiply(scaleVector, g_XMNegateZ);
XMVECTOR scaleNegateXZ = XMVectorMultiply(scaleVector, XMVectorMultiply(g_XMNegateX, g_XMNegateZ));
for (size_t i = 0; i < _countof(TeapotPatches); i++)
{
TeapotPatch const& patch = TeapotPatches[i];
// Because the teapot is symmetrical from left to right, we only store
// data for one side, then tessellate each patch twice, mirroring in X.
TessellatePatch(vertices, indices, patch, tessellation, scaleVector, false);
TessellatePatch(vertices, indices, patch, tessellation, scaleNegateX, true);
if (patch.mirrorZ)
{
// Some parts of the teapot (the body, lid, and rim, but not the
// handle or spout) are also symmetrical from front to back, so
// we tessellate them four times, mirroring in Z as well as X.
TessellatePatch(vertices, indices, patch, tessellation, scaleNegateZ, true);
TessellatePatch(vertices, indices, patch, tessellation, scaleNegateXZ, false);
}
}
// Built RH above
if (!rhcoords)
ReverseWinding(indices, vertices);
}
//--------------------------------------------------------------------------------------
// Dodecahedron
//--------------------------------------------------------------------------------------
void DirectX::ComputeDodecahedron(VertexCollection& vertices, IndexCollection& indices, float size, bool rhcoords)
{
vertices.clear();
indices.clear();
static const float a = 1.f / SQRT3;
static const float b = 0.356822089773089931942f; // sqrt( ( 3 - sqrt(5) ) / 6 )
static const float c = 0.934172358962715696451f; // sqrt( ( 3 + sqrt(5) ) / 6 );
static const XMVECTORF32 verts[20] =
{
{ { { a, a, a, 0 } } },
{ { { a, a, -a, 0 } } },
{ { { a, -a, a, 0 } } },
{ { { a, -a, -a, 0 } } },
{ { { -a, a, a, 0 } } },
{ { { -a, a, -a, 0 } } },
{ { { -a, -a, a, 0 } } },
{ { { -a, -a, -a, 0 } } },
{ { { b, c, 0, 0 } } },
{ { { -b, c, 0, 0 } } },
{ { { b, -c, 0, 0 } } },
{ { { -b, -c, 0, 0 } } },
{ { { c, 0, b, 0 } } },
{ { { c, 0, -b, 0 } } },
{ { { -c, 0, b, 0 } } },
{ { { -c, 0, -b, 0 } } },
{ { { 0, b, c, 0 } } },
{ { { 0, -b, c, 0 } } },
{ { { 0, b, -c, 0 } } },
{ { { 0, -b, -c, 0 } } }
};
static const uint32_t faces[12 * 5] =
{
0, 8, 9, 4, 16,
0, 16, 17, 2, 12,
12, 2, 10, 3, 13,
9, 5, 15, 14, 4,
3, 19, 18, 1, 13,
7, 11, 6, 14, 15,
0, 12, 13, 1, 8,
8, 1, 18, 5, 9,
16, 4, 14, 6, 17,
6, 11, 10, 2, 17,
7, 15, 5, 18, 19,
7, 19, 3, 10, 11,
};
static const XMVECTORF32 textureCoordinates[5] =
{
{ { { 0.654508f, 0.0244717f, 0, 0 } } },
{ { { 0.0954915f, 0.206107f, 0, 0 } } },
{ { { 0.0954915f, 0.793893f, 0, 0 } } },
{ { { 0.654508f, 0.975528f, 0, 0 } } },
{ { { 1.f, 0.5f, 0, 0 } } }
};
static const uint32_t textureIndex[12][5] =
{
{ 0, 1, 2, 3, 4 },
{ 2, 3, 4, 0, 1 },
{ 4, 0, 1, 2, 3 },
{ 1, 2, 3, 4, 0 },
{ 2, 3, 4, 0, 1 },
{ 0, 1, 2, 3, 4 },
{ 1, 2, 3, 4, 0 },
{ 4, 0, 1, 2, 3 },
{ 4, 0, 1, 2, 3 },
{ 1, 2, 3, 4, 0 },
{ 0, 1, 2, 3, 4 },
{ 2, 3, 4, 0, 1 },
};
size_t t = 0;
for (size_t j = 0; j < _countof(faces); j += 5, ++t)
{
uint32_t v0 = faces[j];
uint32_t v1 = faces[j + 1];
uint32_t v2 = faces[j + 2];
uint32_t v3 = faces[j + 3];
uint32_t v4 = faces[j + 4];
XMVECTOR normal = XMVector3Cross(
XMVectorSubtract(verts[v1].v, verts[v0].v),
XMVectorSubtract(verts[v2].v, verts[v0].v));
normal = XMVector3Normalize(normal);
size_t base = vertices.size();
index_push_back(indices, base);
index_push_back(indices, base + 1);
index_push_back(indices, base + 2);
index_push_back(indices, base);
index_push_back(indices, base + 2);
index_push_back(indices, base + 3);
index_push_back(indices, base);
index_push_back(indices, base + 3);
index_push_back(indices, base + 4);
// Duplicate vertices to use face normals
XMVECTOR position = XMVectorScale(verts[v0], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinates[textureIndex[t][0]]));
position = XMVectorScale(verts[v1], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinates[textureIndex[t][1]]));
position = XMVectorScale(verts[v2], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinates[textureIndex[t][2]]));
position = XMVectorScale(verts[v3], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinates[textureIndex[t][3]]));
position = XMVectorScale(verts[v4], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinates[textureIndex[t][4]]));
}
// Built LH above
if (rhcoords)
ReverseWinding(indices, vertices);
assert(vertices.size() == 12 * 5);
assert(indices.size() == 12 * 3 * 3);
}
//--------------------------------------------------------------------------------------
// Cube (aka a Hexahedron) or Box
//--------------------------------------------------------------------------------------
void DirectX::ComputeBox(VertexCollection& vertices, IndexCollection& indices, const XMFLOAT3& size, bool rhcoords, bool invertn)
{
vertices.clear();
indices.clear();
// A box has six faces, each one pointing in a different direction.
const int FaceCount = 6;
static const XMVECTORF32 faceNormals[FaceCount] =
{
{ { { 0, 0, 1, 0 } } },
{ { { 0, 0, -1, 0 } } },
{ { { 1, 0, 0, 0 } } },
{ { { -1, 0, 0, 0 } } },
{ { { 0, 1, 0, 0 } } },
{ { { 0, -1, 0, 0 } } },
};
static const XMVECTORF32 textureCoordinates[4] =
{
{ { { 1, 0, 0, 0 } } },
{ { { 1, 1, 0, 0 } } },
{ { { 0, 1, 0, 0 } } },
{ { { 0, 0, 0, 0 } } },
};
XMVECTOR tsize = XMLoadFloat3(&size);
tsize = XMVectorDivide(tsize, g_XMTwo);
// Create each face in turn.
for (int i = 0; i < FaceCount; i++)
{
XMVECTOR normal = faceNormals[i];
// Get two vectors perpendicular both to the face normal and to each other.
XMVECTOR basis = (i >= 4) ? g_XMIdentityR2 : g_XMIdentityR1;
XMVECTOR side1 = XMVector3Cross(normal, basis);
XMVECTOR side2 = XMVector3Cross(normal, side1);
// Six indices (two triangles) per face.
size_t vbase = vertices.size();
index_push_back(indices, vbase + 0);
index_push_back(indices, vbase + 1);
index_push_back(indices, vbase + 2);
index_push_back(indices, vbase + 0);
index_push_back(indices, vbase + 2);
index_push_back(indices, vbase + 3);
// Four vertices per face.
// (normal - side1 - side2) * tsize // normal // t0
vertices.push_back(VertexPositionNormalTexture(XMVectorMultiply(XMVectorSubtract(XMVectorSubtract(normal, side1), side2), tsize), normal, textureCoordinates[0]));
// (normal - side1 + side2) * tsize // normal // t1
vertices.push_back(VertexPositionNormalTexture(XMVectorMultiply(XMVectorAdd(XMVectorSubtract(normal, side1), side2), tsize), normal, textureCoordinates[1]));
// (normal + side1 + side2) * tsize // normal // t2
vertices.push_back(VertexPositionNormalTexture(XMVectorMultiply(XMVectorAdd(normal, XMVectorAdd(side1, side2)), tsize), normal, textureCoordinates[2]));
// (normal + side1 - side2) * tsize // normal // t3
vertices.push_back(VertexPositionNormalTexture(XMVectorMultiply(XMVectorSubtract(XMVectorAdd(normal, side1), side2), tsize), normal, textureCoordinates[3]));
}
// Build RH above
if (!rhcoords)
ReverseWinding(indices, vertices);
if (invertn)
InvertNormals(vertices);
}
//--------------------------------------------------------------------------------------
// Geodesic sphere
//--------------------------------------------------------------------------------------
void DirectX::ComputeGeoSphere(VertexCollection& vertices, IndexCollection& indices, float diameter, size_t tessellation, bool rhcoords)
{
vertices.clear();
indices.clear();
// An undirected edge between two vertices, represented by a pair of indexes into a vertex array.
// Becuse this edge is undirected, (a,b) is the same as (b,a).
typedef std::pair<uint16_t, uint16_t> UndirectedEdge;
// Makes an undirected edge. Rather than overloading comparison operators to give us the (a,b)==(b,a) property,
// we'll just ensure that the larger of the two goes first. This'll simplify things greatly.
auto makeUndirectedEdge = [](uint16_t a, uint16_t b)
{
return std::make_pair(std::max(a, b), std::min(a, b));
};
// Key: an edge
// Value: the index of the vertex which lies midway between the two vertices pointed to by the key value
// This map is used to avoid duplicating vertices when subdividing triangles along edges.
typedef std::map<UndirectedEdge, uint16_t> EdgeSubdivisionMap;
static const XMFLOAT3 OctahedronVertices[] =
{
// when looking down the negative z-axis (into the screen)
XMFLOAT3(0, 1, 0), // 0 top
XMFLOAT3(0, 0, -1), // 1 front
XMFLOAT3(1, 0, 0), // 2 right
XMFLOAT3(0, 0, 1), // 3 back
XMFLOAT3(-1, 0, 0), // 4 left
XMFLOAT3(0, -1, 0), // 5 bottom
};
static const uint16_t OctahedronIndices[] =
{
0, 1, 2, // top front-right face
0, 2, 3, // top back-right face
0, 3, 4, // top back-left face
0, 4, 1, // top front-left face
5, 1, 4, // bottom front-left face
5, 4, 3, // bottom back-left face
5, 3, 2, // bottom back-right face
5, 2, 1, // bottom front-right face
};
const float radius = diameter / 2.0f;
// Start with an octahedron; copy the data into the vertex/index collection.
std::vector<XMFLOAT3> vertexPositions(std::begin(OctahedronVertices), std::end(OctahedronVertices));
indices.insert(indices.begin(), std::begin(OctahedronIndices), std::end(OctahedronIndices));
// We know these values by looking at the above index list for the octahedron. Despite the subdivisions that are
// about to go on, these values aren't ever going to change because the vertices don't move around in the array.
// We'll need these values later on to fix the singularities that show up at the poles.
const uint16_t northPoleIndex = 0;
const uint16_t southPoleIndex = 5;
for (size_t iSubdivision = 0; iSubdivision < tessellation; ++iSubdivision)
{
assert(indices.size() % 3 == 0); // sanity
// We use this to keep track of which edges have already been subdivided.
EdgeSubdivisionMap subdividedEdges;
// The new index collection after subdivision.
IndexCollection newIndices;
const size_t triangleCount = indices.size() / 3;
for (size_t iTriangle = 0; iTriangle < triangleCount; ++iTriangle)
{
// For each edge on this triangle, create a new vertex in the middle of that edge.
// The winding order of the triangles we output are the same as the winding order of the inputs.
// Indices of the vertices making up this triangle
uint16_t iv0 = indices[iTriangle * 3 + 0];
uint16_t iv1 = indices[iTriangle * 3 + 1];
uint16_t iv2 = indices[iTriangle * 3 + 2];
// Get the new vertices
XMFLOAT3 v01; // vertex on the midpoint of v0 and v1
XMFLOAT3 v12; // ditto v1 and v2
XMFLOAT3 v20; // ditto v2 and v0
uint16_t iv01; // index of v01
uint16_t iv12; // index of v12
uint16_t iv20; // index of v20
// Function that, when given the index of two vertices, creates a new vertex at the midpoint of those vertices.
auto divideEdge = [&](uint16_t i0, uint16_t i1, XMFLOAT3& outVertex, uint16_t& outIndex)
{
const UndirectedEdge edge = makeUndirectedEdge(i0, i1);
// Check to see if we've already generated this vertex
auto it = subdividedEdges.find(edge);
if (it != subdividedEdges.end())
{
// We've already generated this vertex before
outIndex = it->second; // the index of this vertex
outVertex = vertexPositions[outIndex]; // and the vertex itself
}
else
{
// Haven't generated this vertex before: so add it now
// outVertex = (vertices[i0] + vertices[i1]) / 2
XMStoreFloat3(
&outVertex,
XMVectorScale(
XMVectorAdd(XMLoadFloat3(&vertexPositions[i0]), XMLoadFloat3(&vertexPositions[i1])),
0.5f
)
);
outIndex = static_cast<uint16_t>(vertexPositions.size());
CheckIndexOverflow(outIndex);
vertexPositions.push_back(outVertex);
// Now add it to the map.
auto entry = std::make_pair(edge, outIndex);
subdividedEdges.insert(entry);
}
};
// Add/get new vertices and their indices
divideEdge(iv0, iv1, v01, iv01);
divideEdge(iv1, iv2, v12, iv12);
divideEdge(iv0, iv2, v20, iv20);
// Add the new indices. We have four new triangles from our original one:
// v0
// o
// /a\
// v20 o---o v01
// /b\c/d\
// v2 o---o---o v1
// v12
const uint16_t indicesToAdd[] =
{
iv0, iv01, iv20, // a
iv20, iv12, iv2, // b
iv20, iv01, iv12, // c
iv01, iv1, iv12, // d
};
newIndices.insert(newIndices.end(), std::begin(indicesToAdd), std::end(indicesToAdd));
}
indices = std::move(newIndices);
}
// Now that we've completed subdivision, fill in the final vertex collection
vertices.reserve(vertexPositions.size());
for (auto it = vertexPositions.begin(); it != vertexPositions.end(); ++it)
{
auto vertexValue = *it;
auto normal = XMVector3Normalize(XMLoadFloat3(&vertexValue));
auto pos = XMVectorScale(normal, radius);
XMFLOAT3 normalFloat3;
XMStoreFloat3(&normalFloat3, normal);
// calculate texture coordinates for this vertex
float longitude = atan2(normalFloat3.x, -normalFloat3.z);
float latitude = acos(normalFloat3.y);
float u = longitude / XM_2PI + 0.5f;
float v = latitude / XM_PI;
auto texcoord = XMVectorSet(1.0f - u, v, 0.0f, 0.0f);
vertices.push_back(VertexPositionNormalTexture(pos, normal, texcoord));
}
// There are a couple of fixes to do. One is a texture coordinate wraparound fixup. At some point, there will be
// a set of triangles somewhere in the mesh with texture coordinates such that the wraparound across 0.0/1.0
// occurs across that triangle. Eg. when the left hand side of the triangle has a U coordinate of 0.98 and the
// right hand side has a U coordinate of 0.0. The intent is that such a triangle should render with a U of 0.98 to
// 1.0, not 0.98 to 0.0. If we don't do this fixup, there will be a visible seam across one side of the sphere.
//
// Luckily this is relatively easy to fix. There is a straight edge which runs down the prime meridian of the
// completed sphere. If you imagine the vertices along that edge, they circumscribe a semicircular arc starting at
// y=1 and ending at y=-1, and sweeping across the range of z=0 to z=1. x stays zero. It's along this edge that we
// need to duplicate our vertices - and provide the correct texture coordinates.
size_t preFixupVertexCount = vertices.size();
for (size_t i = 0; i < preFixupVertexCount; ++i)
{
// This vertex is on the prime meridian if position.x and texcoord.u are both zero (allowing for small epsilon).
bool isOnPrimeMeridian = XMVector2NearEqual(
XMVectorSet(vertices[i].position.x, vertices[i].textureCoordinate.x, 0.0f, 0.0f),
XMVectorZero(),
XMVectorSplatEpsilon());
if (isOnPrimeMeridian)
{
size_t newIndex = vertices.size(); // the index of this vertex that we're about to add
CheckIndexOverflow(newIndex);
// copy this vertex, correct the texture coordinate, and add the vertex
VertexPositionNormalTexture v = vertices[i];
v.textureCoordinate.x = 1.0f;
vertices.push_back(v);
// Now find all the triangles which contain this vertex and update them if necessary
for (size_t j = 0; j < indices.size(); j += 3)
{
uint16_t* triIndex0 = &indices[j + 0];
uint16_t* triIndex1 = &indices[j + 1];
uint16_t* triIndex2 = &indices[j + 2];
if (*triIndex0 == i)
{
// nothing; just keep going
}
else if (*triIndex1 == i)
{
std::swap(triIndex0, triIndex1); // swap the pointers (not the values)
}
else if (*triIndex2 == i)
{
std::swap(triIndex0, triIndex2); // swap the pointers (not the values)
}
else
{
// this triangle doesn't use the vertex we're interested in
continue;
}
// If we got to this point then triIndex0 is the pointer to the index to the vertex we're looking at
assert(*triIndex0 == i);
assert(*triIndex1 != i && *triIndex2 != i); // assume no degenerate triangles
const VertexPositionNormalTexture& v0 = vertices[*triIndex0];
const VertexPositionNormalTexture& v1 = vertices[*triIndex1];
const VertexPositionNormalTexture& v2 = vertices[*triIndex2];
// check the other two vertices to see if we might need to fix this triangle
if (abs(v0.textureCoordinate.x - v1.textureCoordinate.x) > 0.5f ||
abs(v0.textureCoordinate.x - v2.textureCoordinate.x) > 0.5f)
{
// yep; replace the specified index to point to the new, corrected vertex
*triIndex0 = static_cast<uint16_t>(newIndex);
}
}
}
}
// And one last fix we need to do: the poles. A common use-case of a sphere mesh is to map a rectangular texture onto
// it. If that happens, then the poles become singularities which map the entire top and bottom rows of the texture
// onto a single point. In general there's no real way to do that right. But to match the behavior of non-geodesic
// spheres, we need to duplicate the pole vertex for every triangle that uses it. This will introduce seams near the
// poles, but reduce stretching.
auto fixPole = [&](size_t poleIndex)
{
auto poleVertex = vertices[poleIndex];
bool overwrittenPoleVertex = false; // overwriting the original pole vertex saves us one vertex
for (size_t i = 0; i < indices.size(); i += 3)
{
// These pointers point to the three indices which make up this triangle. pPoleIndex is the pointer to the
// entry in the index array which represents the pole index, and the other two pointers point to the other
// two indices making up this triangle.
uint16_t* pPoleIndex;
uint16_t* pOtherIndex0;
uint16_t* pOtherIndex1;
if (indices[i + 0] == poleIndex)
{
pPoleIndex = &indices[i + 0];
pOtherIndex0 = &indices[i + 1];
pOtherIndex1 = &indices[i + 2];
}
else if (indices[i + 1] == poleIndex)
{
pPoleIndex = &indices[i + 1];
pOtherIndex0 = &indices[i + 2];
pOtherIndex1 = &indices[i + 0];
}
else if (indices[i + 2] == poleIndex)
{
pPoleIndex = &indices[i + 2];
pOtherIndex0 = &indices[i + 0];
pOtherIndex1 = &indices[i + 1];
}
else
{
continue;
}
const auto& otherVertex0 = vertices[*pOtherIndex0];
const auto& otherVertex1 = vertices[*pOtherIndex1];
// Calculate the texcoords for the new pole vertex, add it to the vertices and update the index
VertexPositionNormalTexture newPoleVertex = poleVertex;
newPoleVertex.textureCoordinate.x = (otherVertex0.textureCoordinate.x + otherVertex1.textureCoordinate.x) / 2;
newPoleVertex.textureCoordinate.y = poleVertex.textureCoordinate.y;
if (!overwrittenPoleVertex)
{
vertices[poleIndex] = newPoleVertex;
overwrittenPoleVertex = true;
}
else
{
CheckIndexOverflow(vertices.size());
*pPoleIndex = static_cast<uint16_t>(vertices.size());
vertices.push_back(newPoleVertex);
}
}
};
fixPole(northPoleIndex);
fixPole(southPoleIndex);
// Build RH above
if (!rhcoords)
ReverseWinding(indices, vertices);
}
//--------------------------------------------------------------------------------------
// Sphere
//--------------------------------------------------------------------------------------
void DirectX::ComputeSphere(VertexCollection& vertices, IndexCollection& indices, float diameter, size_t tessellation, bool rhcoords, bool invertn)
{
vertices.clear();
indices.clear();
if (tessellation < 3)
throw std::out_of_range("tesselation parameter out of range");
size_t verticalSegments = tessellation;
size_t horizontalSegments = tessellation * 2;
float radius = diameter / 2;
// Create rings of vertices at progressively higher latitudes.
for (size_t i = 0; i <= verticalSegments; i++)
{
float v = 1 - float(i) / verticalSegments;
float latitude = (i * XM_PI / verticalSegments) - XM_PIDIV2;
float dy, dxz;
XMScalarSinCos(&dy, &dxz, latitude);
// Create a single ring of vertices at this latitude.
for (size_t j = 0; j <= horizontalSegments; j++)
{
float u = float(j) / horizontalSegments;
float longitude = j * XM_2PI / horizontalSegments;
float dx, dz;
XMScalarSinCos(&dx, &dz, longitude);
dx *= dxz;
dz *= dxz;
XMVECTOR normal = XMVectorSet(dx, dy, dz, 0);
XMVECTOR textureCoordinate = XMVectorSet(u, v, 0, 0);
vertices.push_back(VertexPositionNormalTexture(XMVectorScale(normal, radius), normal, textureCoordinate));
}
}
// Fill the index buffer with triangles joining each pair of latitude rings.
size_t stride = horizontalSegments + 1;
for (size_t i = 0; i < verticalSegments; i++)
{
for (size_t j = 0; j <= horizontalSegments; j++)
{
size_t nextI = i + 1;
size_t nextJ = (j + 1) % stride;
index_push_back(indices, i * stride + j);
index_push_back(indices, nextI * stride + j);
index_push_back(indices, i * stride + nextJ);
index_push_back(indices, i * stride + nextJ);
index_push_back(indices, nextI * stride + j);
index_push_back(indices, nextI * stride + nextJ);
}
}
// Build RH above
if (!rhcoords)
ReverseWinding(indices, vertices);
if (invertn)
InvertNormals(vertices);
}
//--------------------------------------------------------------------------------------
// Icosahedron
//--------------------------------------------------------------------------------------
void DirectX::ComputeIcosahedron(VertexCollection& vertices, IndexCollection& indices, float size, bool rhcoords)
{
vertices.clear();
indices.clear();
static const float t = 1.618033988749894848205f; // (1 + sqrt(5)) / 2
static const float t2 = 1.519544995837552493271f; // sqrt( 1 + sqr( (1 + sqrt(5)) / 2 ) )
static const XMVECTORF32 verts[12] =
{
{ { { t / t2, 1.f / t2, 0, 0 } } },
{ { { -t / t2, 1.f / t2, 0, 0 } } },
{ { { t / t2, -1.f / t2, 0, 0 } } },
{ { { -t / t2, -1.f / t2, 0, 0 } } },
{ { { 1.f / t2, 0, t / t2, 0 } } },
{ { { 1.f / t2, 0, -t / t2, 0 } } },
{ { { -1.f / t2, 0, t / t2, 0 } } },
{ { { -1.f / t2, 0, -t / t2, 0 } } },
{ { { 0, t / t2, 1.f / t2, 0 } } },
{ { { 0, -t / t2, 1.f / t2, 0 } } },
{ { { 0, t / t2, -1.f / t2, 0 } } },
{ { { 0, -t / t2, -1.f / t2, 0 } } }
};
static const uint32_t faces[20 * 3] =
{
0, 8, 4,
0, 5, 10,
2, 4, 9,
2, 11, 5,
1, 6, 8,
1, 10, 7,
3, 9, 6,
3, 7, 11,
0, 10, 8,
1, 8, 10,
2, 9, 11,
3, 11, 9,
4, 2, 0,
5, 0, 2,
6, 1, 3,
7, 3, 1,
8, 6, 4,
9, 4, 6,
10, 5, 7,
11, 7, 5
};
for (size_t j = 0; j < _countof(faces); j += 3)
{
uint32_t v0 = faces[j];
uint32_t v1 = faces[j + 1];
uint32_t v2 = faces[j + 2];
XMVECTOR normal = XMVector3Cross(
XMVectorSubtract(verts[v1].v, verts[v0].v),
XMVectorSubtract(verts[v2].v, verts[v0].v));
normal = XMVector3Normalize(normal);
size_t base = vertices.size();
index_push_back(indices, base);
index_push_back(indices, base + 1);
index_push_back(indices, base + 2);
// Duplicate vertices to use face normals
XMVECTOR position = XMVectorScale(verts[v0], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, g_XMZero /* 0, 0 */));
position = XMVectorScale(verts[v1], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, g_XMIdentityR0 /* 1, 0 */));
position = XMVectorScale(verts[v2], size);
vertices.push_back(VertexPositionNormalTexture(position, normal, g_XMIdentityR1 /* 0, 1 */));
}
// Built LH above
if (rhcoords)
ReverseWinding(indices, vertices);
assert(vertices.size() == 20 * 3);
assert(indices.size() == 20 * 3);
}
