//-------------------------------------------------------------------------------------- // File: Geometry.cpp // // Copyright (c) Microsoft Corporation. All rights reserved. // Licensed under the MIT License. // // http://go.microsoft.com/fwlink/?LinkId=248929 // http://go.microsoft.com/fwlink/?LinkID=615561 //-------------------------------------------------------------------------------------- #include "pch.h" #include "Geometry.h" #include "Bezier.h" using namespace DirectX; namespace { constexpr float SQRT2 = 1.41421356237309504880f; constexpr float SQRT3 = 1.73205080756887729352f; constexpr float SQRT6 = 2.44948974278317809820f; inline void CheckIndexOverflow(size_t value) { // Use >=, not > comparison, because some D3D level 9_x hardware does not support 0xFFFF index values. if (value >= USHRT_MAX) throw std::out_of_range("Index value out of range: cannot tesselate primitive so finely"); } // Collection types used when generating the geometry. inline void index_push_back(IndexCollection& indices, size_t value) { CheckIndexOverflow(value); indices.push_back(static_cast(value)); } // Helper for flipping winding of geometric primitives for LH vs. RH coords inline void ReverseWinding(IndexCollection& indices, VertexCollection& vertices) { assert((indices.size() % 3) == 0); for (auto it = indices.begin(); it != indices.end(); it += 3) { std::swap(*it, *(it + 2)); } for (auto it = vertices.begin(); it != vertices.end(); ++it) { it->textureCoordinate.x = (1.f - it->textureCoordinate.x); } } // Helper for inverting normals of geometric primitives for 'inside' vs. 'outside' viewing inline void InvertNormals(VertexCollection& vertices) { for (auto it = vertices.begin(); it != vertices.end(); ++it) { it->normal.x = -it->normal.x; it->normal.y = -it->normal.y; it->normal.z = -it->normal.z; } } } //-------------------------------------------------------------------------------------- // 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. constexpr 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); } //-------------------------------------------------------------------------------------- // 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::invalid_argument("tesselation parameter must be at least 3"); 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) / float(verticalSegments); float latitude = (float(i) * XM_PI / float(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) / float(horizontalSegments); float longitude = float(j) * XM_2PI / float(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); } //-------------------------------------------------------------------------------------- // 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). using UndirectedEdge = std::pair; // 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) noexcept { 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. using EdgeSubdivisionMap = std::map; 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 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(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) { const 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 = atan2f(normalFloat3.x, -normalFloat3.z); float latitude = acosf(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(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) { const 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(vertices.size()); vertices.push_back(newPoleVertex); } } }; fixPole(northPoleIndex); fixPole(southPoleIndex); // Build RH above if (!rhcoords) ReverseWinding(indices, vertices); } //-------------------------------------------------------------------------------------- // Cylinder / Cone //-------------------------------------------------------------------------------------- namespace { // Helper computes a point on a unit circle, aligned to the x/z plane and centered on the origin. inline XMVECTOR GetCircleVector(size_t i, size_t tessellation) noexcept { float angle = float(i) * XM_2PI / float(tessellation); float dx, dz; XMScalarSinCos(&dx, &dz, angle); XMVECTORF32 v = { { { dx, 0, dz, 0 } } }; return v; } inline XMVECTOR GetCircleTangent(size_t i, size_t tessellation) noexcept { float angle = (float(i) * XM_2PI / float(tessellation)) + XM_PIDIV2; float dx, dz; XMScalarSinCos(&dx, &dz, angle); XMVECTORF32 v = { { { dx, 0, dz, 0 } } }; return v; } // Helper creates a triangle fan to close the end of a cylinder / cone void CreateCylinderCap(VertexCollection& vertices, IndexCollection& indices, size_t tessellation, float height, float radius, bool isTop) { // Create cap indices. for (size_t i = 0; i < tessellation - 2; i++) { size_t i1 = (i + 1) % tessellation; size_t i2 = (i + 2) % tessellation; if (isTop) { std::swap(i1, i2); } size_t vbase = vertices.size(); index_push_back(indices, vbase); index_push_back(indices, vbase + i1); index_push_back(indices, vbase + i2); } // Which end of the cylinder is this? XMVECTOR normal = g_XMIdentityR1; XMVECTOR textureScale = g_XMNegativeOneHalf; if (!isTop) { normal = XMVectorNegate(normal); textureScale = XMVectorMultiply(textureScale, g_XMNegateX); } // Create cap vertices. for (size_t i = 0; i < tessellation; i++) { XMVECTOR circleVector = GetCircleVector(i, tessellation); XMVECTOR position = XMVectorAdd(XMVectorScale(circleVector, radius), XMVectorScale(normal, height)); XMVECTOR textureCoordinate = XMVectorMultiplyAdd(XMVectorSwizzle<0, 2, 3, 3>(circleVector), textureScale, g_XMOneHalf); vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinate)); } } } void DirectX::ComputeCylinder(VertexCollection& vertices, IndexCollection& indices, float height, float diameter, size_t tessellation, bool rhcoords) { vertices.clear(); indices.clear(); if (tessellation < 3) throw std::invalid_argument("tesselation parameter must be at least 3"); 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 cylinder. for (size_t i = 0; i <= tessellation; i++) { XMVECTOR normal = GetCircleVector(i, tessellation); XMVECTOR sideOffset = XMVectorScale(normal, radius); float u = float(i) / float(tessellation); XMVECTOR textureCoordinate = XMLoadFloat(&u); vertices.push_back(VertexPositionNormalTexture(XMVectorAdd(sideOffset, topOffset), normal, textureCoordinate)); vertices.push_back(VertexPositionNormalTexture(XMVectorSubtract(sideOffset, topOffset), normal, XMVectorAdd(textureCoordinate, g_XMIdentityR1))); index_push_back(indices, i * 2); index_push_back(indices, (i * 2 + 2) % (stride * 2)); index_push_back(indices, i * 2 + 1); index_push_back(indices, i * 2 + 1); index_push_back(indices, (i * 2 + 2) % (stride * 2)); index_push_back(indices, (i * 2 + 3) % (stride * 2)); } // Create flat triangle fan caps to seal the top and bottom. CreateCylinderCap(vertices, indices, tessellation, height, radius, true); CreateCylinderCap(vertices, indices, tessellation, height, radius, false); // Build RH above if (!rhcoords) ReverseWinding(indices, vertices); } // 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::invalid_argument("tesselation parameter must be at least 3"); 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) / float(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); } //-------------------------------------------------------------------------------------- // 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::invalid_argument("tesselation parameter must be at least 3"); 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) / float(tessellation); float outerAngle = float(i) * XM_2PI / float(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) / float(tessellation); float innerAngle = float(j) * XM_2PI / float(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 < std::size(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); } //-------------------------------------------------------------------------------------- // Octahedron //-------------------------------------------------------------------------------------- void DirectX::ComputeOctahedron(VertexCollection& vertices, IndexCollection& indices, float size, bool rhcoords) { vertices.clear(); indices.clear(); static const XMVECTORF32 verts[6] = { { { { 1, 0, 0, 0 } } }, { { { -1, 0, 0, 0 } } }, { { { 0, 1, 0, 0 } } }, { { { 0, -1, 0, 0 } } }, { { { 0, 0, 1, 0 } } }, { { { 0, 0, -1, 0 } } } }; static const uint32_t faces[8 * 3] = { 4, 0, 2, 4, 2, 1, 4, 1, 3, 4, 3, 0, 5, 2, 0, 5, 1, 2, 5, 3, 1, 5, 0, 3 }; for (size_t j = 0; j < std::size(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() == 8 * 3); assert(indices.size() == 8 * 3); } //-------------------------------------------------------------------------------------- // 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 < std::size(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); } //-------------------------------------------------------------------------------------- // 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 < std::size(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); } //-------------------------------------------------------------------------------------- // Teapot //-------------------------------------------------------------------------------------- // Include the teapot control point data. namespace { #include "TeapotData.inc" // Tessellates the specified bezier patch. void XM_CALLCONV TessellatePatch(VertexCollection& vertices, IndexCollection& indices, TeapotPatch const& patch, size_t tessellation, FXMVECTOR scale, bool isMirrored) { // Look up the 16 control points for this patch. XMVECTOR controlPoints[16] = {}; for (int i = 0; i < 16; i++) { controlPoints[i] = XMVectorMultiply(TeapotControlPoints[patch.indices[i]], scale); } // Create the index data. size_t vbase = vertices.size(); Bezier::CreatePatchIndices(tessellation, isMirrored, [&](size_t index) { index_push_back(indices, vbase + index); }); // Create the vertex data. Bezier::CreatePatchVertices(controlPoints, tessellation, isMirrored, [&](FXMVECTOR position, FXMVECTOR normal, FXMVECTOR textureCoordinate) { vertices.push_back(VertexPositionNormalTexture(position, normal, textureCoordinate)); }); } } // 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::invalid_argument("tesselation parameter must be non-zero"); 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 < std::size(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); }