nh-rep/code/pre_processing/ParametricSample/Mathematics/RectangleMesh.h

// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2021
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2019.08.13

#pragma once

#include <Mathematics/Mesh.h>
#include <Mathematics/Rectangle.h>
#include <Mathematics/Vector3.h>
#include <memory>

namespace gte
{
    template <typename Real>
    class RectangleMesh : public Mesh<Real>
    {
    public:
        // Create a mesh that tessellates a rectangle.
        RectangleMesh(MeshDescription const& description, Rectangle<3, Real> const& rectangle)
            :
            Mesh<Real>(description, { MeshTopology::RECTANGLE }),
            mRectangle(rectangle)
        {
            if (!this->mDescription.constructed)
            {
                // The logger system will report these errors in the Mesh
                // constructor.
                return;
            }

            if (!this->mTCoords)
            {
                mDefaultTCoords.resize(this->mDescription.numVertices);
                this->mTCoords = mDefaultTCoords.data();
                this->mTCoordStride = sizeof(Vector2<Real>);

                this->mDescription.allowUpdateFrame = this->mDescription.wantDynamicTangentSpaceUpdate;
                if (this->mDescription.allowUpdateFrame)
                {
                    if (!this->mDescription.hasTangentSpaceVectors)
                    {
                        this->mDescription.allowUpdateFrame = false;
                    }

                    if (!this->mNormals)
                    {
                        this->mDescription.allowUpdateFrame = false;
                    }
                }
            }

            this->ComputeIndices();
            InitializeTCoords();
            InitializePositions();
            if (this->mDescription.allowUpdateFrame)
            {
                InitializeFrame();
            }
            else if (this->mNormals)
            {
                InitializeNormals();
            }
        }

        // Member access.
        inline Rectangle<3, Real> const& GetRectangle() const
        {
            return mRectangle;
        }

    protected:
        void InitializeTCoords()
        {
            Vector2<Real> tcoord;
            for (uint32_t r = 0, i = 0; r < this->mDescription.numRows; ++r)
            {
                tcoord[1] = (Real)r / (Real)(this->mDescription.numRows - 1);
                for (uint32_t c = 0; c < this->mDescription.numCols; ++c, ++i)
                {
                    tcoord[0] = (Real)c / (Real)(this->mDescription.numCols - 1);
                    this->TCoord(i) = tcoord;
                }
            }
        }

        void InitializePositions()
        {
            for (uint32_t r = 0, i = 0; r < this->mDescription.numRows; ++r)
            {
                for (uint32_t c = 0; c < this->mDescription.numCols; ++c, ++i)
                {
                    Vector2<Real> tcoord = this->TCoord(i);
                    Real w0 = ((Real)2 * tcoord[0] - (Real)1) * mRectangle.extent[0];
                    Real w1 = ((Real)2 * tcoord[1] - (Real)1) * mRectangle.extent[1];
                    this->Position(i) = mRectangle.center + w0 * mRectangle.axis[0] + w1 * mRectangle.axis[1];
                }
            }
        }

        void InitializeNormals()
        {
            Vector3<Real> normal = UnitCross(mRectangle.axis[0], mRectangle.axis[1]);
            for (uint32_t i = 0; i < this->mDescription.numVertices; ++i)
            {
                this->Normal(i) = normal;
            }
        }

        void InitializeFrame()
        {
            Vector3<Real> normal = UnitCross(mRectangle.axis[0], mRectangle.axis[1]);
            Vector3<Real> tangent{ (Real)1, (Real)0, (Real)0 };
            Vector3<Real> bitangent{ (Real)0, (Real)1, (Real)0 };
            // bitangent = Cross(normal,tangent)
            // TODO: Are tangent and bitangent correct?
            for (uint32_t i = 0; i < this->mDescription.numVertices; ++i)
            {
                if (this->mNormals)
                {
                    this->Normal(i) = normal;
                }

                if (this->mTangents)
                {
                    this->Tangent(i) = tangent;
                }

                if (this->mBitangents)
                {
                    this->Bitangent(i) = bitangent;
                }

                if (this->mDPDUs)
                {
                    this->DPDU(i) = tangent;
                }

                if (this->mDPDVs)
                {
                    this->DPDV(i) = bitangent;
                }
            }
        }

        Rectangle<3, Real> mRectangle;

        // If the client does not request texture coordinates, they will be
        // computed internally for use in evaluation of the surface geometry.
        std::vector<Vector2<Real>> mDefaultTCoords;
    };
}