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318 lines
12 KiB
318 lines
12 KiB
3 months ago
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// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/Mesh.h>
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#include <Mathematics/ParametricCurve.h>
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#include <memory>
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namespace gte
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{
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template <typename Real>
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class RevolutionMesh : public Mesh<Real>
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{
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public:
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// The axis of revolution is the z-axis. The curve of revolution is
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// p(t) = (x(t),z(t)), where t in [tmin,tmax], x(t) > 0 for t in
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// (tmin,tmax), x(tmin) >= 0, and x(tmax) >= 0. The values tmin and
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// tmax are those for the curve object passed to the constructor. The
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// curve must be non-self-intersecting, except possibly at its
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// endpoints. The curve is closed when p(tmin) = p(tmax), in which
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// case the surface of revolution has torus topology. The curve is
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// open when p(tmin) != p(tmax). For an open curve, define
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// x0 = x(tmin) and x1 = x(tmax). The surface has cylinder topology
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// when x0 > 0 and x1 > 0, disk topology when exactly one of x0 or x1
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// is zero, or sphere topology when x0 and x1 are both zero. However,
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// to simplify the design, the mesh is always built using cylinder
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// topology. The row samples correspond to curve points and the
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// column samples correspond to the points on the circles of
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// revolution.
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RevolutionMesh(MeshDescription const& description,
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std::shared_ptr<ParametricCurve<2, Real>> const& curve,
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bool sampleByArcLength = false)
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:
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Mesh<Real>(description,
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{ MeshTopology::CYLINDER, MeshTopology::TORUS, MeshTopology::DISK, MeshTopology::SPHERE }),
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mCurve(curve),
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mSampleByArcLength(sampleByArcLength)
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{
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if (!this->mDescription.constructed)
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{
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// The logger system will report these errors in the Mesh
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// constructor.
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mCurve = nullptr;
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return;
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}
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LogAssert(mCurve != nullptr, "A nonnull revolution curve is required.");
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// The four supported topologies all wrap around in the column
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// direction.
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mCosAngle.resize(this->mDescription.numCols + 1);
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mSinAngle.resize(this->mDescription.numCols + 1);
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Real invRadialSamples = (Real)1 / (Real)this->mDescription.numCols;
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for (unsigned int c = 0; c < this->mDescription.numCols; ++c)
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{
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Real angle = c * invRadialSamples * (Real)GTE_C_TWO_PI;
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mCosAngle[c] = std::cos(angle);
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mSinAngle[c] = std::sin(angle);
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}
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mCosAngle[this->mDescription.numCols] = mCosAngle[0];
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mSinAngle[this->mDescription.numCols] = mSinAngle[0];
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CreateSampler();
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if (!this->mTCoords)
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{
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mDefaultTCoords.resize(this->mDescription.numVertices);
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this->mTCoords = mDefaultTCoords.data();
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this->mTCoordStride = sizeof(Vector2<Real>);
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this->mDescription.allowUpdateFrame = this->mDescription.wantDynamicTangentSpaceUpdate;
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if (this->mDescription.allowUpdateFrame)
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{
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if (!this->mDescription.hasTangentSpaceVectors)
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{
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this->mDescription.allowUpdateFrame = false;
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}
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if (!this->mNormals)
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{
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this->mDescription.allowUpdateFrame = false;
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}
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}
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}
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this->ComputeIndices();
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InitializeTCoords();
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UpdatePositions();
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if (this->mDescription.allowUpdateFrame)
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{
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this->UpdateFrame();
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}
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else if (this->mNormals)
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{
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this->UpdateNormals();
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}
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}
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// Member access.
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inline std::shared_ptr<ParametricCurve<2, Real>> const& GetCurve() const
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{
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return mCurve;
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}
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inline bool IsSampleByArcLength() const
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{
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return mSampleByArcLength;
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}
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private:
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void CreateSampler()
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{
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if (this->mDescription.topology == MeshTopology::CYLINDER
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|| this->mDescription.topology == MeshTopology::TORUS)
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{
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mSamples.resize(this->mDescription.rMax + 1);
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}
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else if (this->mDescription.topology == MeshTopology::DISK)
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{
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mSamples.resize(this->mDescription.rMax + 2);
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}
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else if (this->mDescription.topology == MeshTopology::SPHERE)
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{
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mSamples.resize(this->mDescription.rMax + 3);
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}
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Real invDenom = ((Real)1) / (Real)(mSamples.size() - 1);
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if (mSampleByArcLength)
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{
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Real factor = mCurve->GetTotalLength() * invDenom;
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mTSampler = [this, factor](unsigned int i)
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{
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return mCurve->GetTime(i * factor);
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};
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}
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else
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{
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Real factor = (mCurve->GetTMax() - mCurve->GetTMin()) * invDenom;
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mTSampler = [this, factor](unsigned int i)
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{
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return mCurve->GetTMin() + i * factor;
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};
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}
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}
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void InitializeTCoords()
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{
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Vector2<Real>tcoord;
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switch (this->mDescription.topology)
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{
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case MeshTopology::CYLINDER:
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{
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for (unsigned int r = 0, i = 0; r < this->mDescription.numRows; ++r)
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{
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tcoord[1] = (Real)r / (Real)(this->mDescription.numRows - 1);
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for (unsigned int c = 0; c <= this->mDescription.numCols; ++c, ++i)
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{
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tcoord[0] = (Real)c / (Real)this->mDescription.numCols;
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this->TCoord(i) = tcoord;
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}
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}
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break;
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}
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case MeshTopology::TORUS:
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{
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for (unsigned int r = 0, i = 0; r <= this->mDescription.numRows; ++r)
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{
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tcoord[1] = (Real)r / (Real)this->mDescription.numRows;
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for (unsigned int c = 0; c <= this->mDescription.numCols; ++c, ++i)
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{
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tcoord[0] = (Real)c / (Real)this->mDescription.numCols;
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this->TCoord(i) = tcoord;
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}
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}
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break;
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}
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case MeshTopology::DISK:
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{
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Vector2<Real> origin{ (Real)0.5, (Real)0.5 };
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unsigned int i = 0;
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for (unsigned int r = 0; r < this->mDescription.numRows; ++r)
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{
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Real radius = (Real)(r + 1) / (Real)(2 * this->mDescription.numRows);
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radius = std::min(radius, (Real)0.5);
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for (unsigned int c = 0; c <= this->mDescription.numCols; ++c, ++i)
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{
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Real angle = (Real)GTE_C_TWO_PI * (Real)c / (Real)this->mDescription.numCols;
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this->TCoord(i) = { radius * std::cos(angle), radius * std::sin(angle) };
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}
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}
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this->TCoord(i) = origin;
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break;
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}
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case MeshTopology::SPHERE:
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{
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unsigned int i = 0;
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for (unsigned int r = 0; r < this->mDescription.numRows; ++r)
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{
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tcoord[1] = (Real)r / (Real)(this->mDescription.numRows - 1);
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for (unsigned int c = 0; c <= this->mDescription.numCols; ++c, ++i)
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{
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tcoord[0] = (Real)c / (Real)this->mDescription.numCols;
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this->TCoord(i) = tcoord;
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}
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}
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this->TCoord(i++) = { (Real)0.5, (Real)0 };
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this->TCoord(i) = { (Real)0.5, (Real)1 };
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break;
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}
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default:
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// Invalid topology is reported by the Mesh constructor, so there is
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// no need to log a message here.
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break;
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}
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}
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virtual void UpdatePositions() override
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{
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unsigned int const numSamples = static_cast<unsigned int>(mSamples.size());
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for (unsigned int i = 0; i < numSamples; ++i)
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{
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Real t = mTSampler(i);
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Vector2<Real> position = mCurve->GetPosition(t);
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mSamples[i][0] = position[0];
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mSamples[i][1] = (Real)0;
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mSamples[i][2] = position[1];
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}
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switch (this->mDescription.topology)
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{
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case MeshTopology::CYLINDER:
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UpdateCylinderPositions();
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break;
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case MeshTopology::TORUS:
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UpdateTorusPositions();
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break;
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case MeshTopology::DISK:
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UpdateDiskPositions();
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break;
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case MeshTopology::SPHERE:
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UpdateSpherePositions();
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break;
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default:
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break;
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}
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}
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void UpdateCylinderPositions()
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{
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for (unsigned int r = 0, i = 0; r <= this->mDescription.rMax; ++r)
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{
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Real radius = mSamples[r][0];
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for (unsigned int c = 0; c <= this->mDescription.cMax; ++c, ++i)
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{
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this->Position(i) = { radius * mCosAngle[c], radius * mSinAngle[c], mSamples[r][2] };
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}
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}
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}
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void UpdateTorusPositions()
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{
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for (unsigned int r = 0, i = 0; r <= this->mDescription.rMax; ++r)
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{
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Real radius = mSamples[r][0];
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for (unsigned int c = 0; c <= this->mDescription.cMax; ++c, ++i)
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{
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this->Position(i) = { radius * mCosAngle[c], radius * mSinAngle[c], mSamples[r][2] };
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}
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}
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}
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void UpdateDiskPositions()
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{
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for (unsigned int r = 0, rp1 = 1, i = 0; r <= this->mDescription.rMax; ++r, ++rp1)
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{
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Real radius = mSamples[rp1][0];
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for (unsigned int c = 0; c <= this->mDescription.cMax; ++c, ++i)
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{
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this->Position(i) = { radius * mCosAngle[c], radius * mSinAngle[c], mSamples[rp1][2] };
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}
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}
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this->Position(this->mDescription.numVertices - 1) = { (Real)0, (Real)0, mSamples.front()[2] };
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}
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void UpdateSpherePositions()
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{
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for (unsigned int r = 0, rp1 = 1, i = 0; r <= this->mDescription.rMax; ++r, ++rp1)
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{
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Real radius = mSamples[rp1][0];
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for (unsigned int c = 0; c <= this->mDescription.cMax; ++c, ++i)
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{
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this->Position(i) = { radius * mCosAngle[c], radius * mSinAngle[c], mSamples[rp1][2] };
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}
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}
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this->Position(this->mDescription.numVertices - 2) = { (Real)0, (Real)0, mSamples.front()[2] };
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this->Position(this->mDescription.numVertices - 1) = { (Real)0, (Real)0, mSamples.back()[2] };
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}
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std::shared_ptr<ParametricCurve<2, Real>> mCurve;
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bool mSampleByArcLength;
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std::vector<Real> mCosAngle, mSinAngle;
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std::function<Real(unsigned int)> mTSampler;
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std::vector<Vector3<Real>> mSamples;
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// If the client does not request texture coordinates, they will be
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// computed internally for use in evaluation of the surface geometry.
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std::vector<Vector2<Real>> mDefaultTCoords;
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};
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}
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