text: /*
  Open Asset Import Library (assimp)
  ----------------------------------------------------------------------
  
  Copyright (c) 2006-2020, assimp team
  
  
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    copyright notice, this list of conditions and the
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  OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
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  */
  
  /** @file   StandardShapes.cpp
   *  @brief  Implementation of the StandardShapes class
   *
   *  The primitive geometry data comes from
   *  http://geometrictools.com/Documentation/PlatonicSolids.pdf.
   */
  
  #include <assimp/StandardShapes.h>
  #include <assimp/StringComparison.h>
  #include <stddef.h>
  #include <assimp/Defines.h>
  #include <assimp/mesh.h>
  
  namespace Assimp    {
  
  
  # define ADD_TRIANGLE(n0,n1,n2) \
      positions.push_back(n0); \
      positions.push_back(n1); \
      positions.push_back(n2);
  
  #   define ADD_PENTAGON(n0,n1,n2,n3,n4) \
      if (polygons) \
      { \
          positions.push_back(n0); \
          positions.push_back(n1); \
          positions.push_back(n2); \
          positions.push_back(n3); \
          positions.push_back(n4); \
      } \
      else \
      { \
          ADD_TRIANGLE(n0, n1, n2) \
          ADD_TRIANGLE(n0, n2, n3) \
          ADD_TRIANGLE(n0, n3, n4) \
      }
  
  #   define ADD_QUAD(n0,n1,n2,n3) \
      if (polygons) \
      { \
          positions.push_back(n0); \
          positions.push_back(n1); \
          positions.push_back(n2); \
          positions.push_back(n3); \
      } \
      else \
      { \
          ADD_TRIANGLE(n0, n1, n2) \
          ADD_TRIANGLE(n0, n2, n3) \
      }
  
  
  // ------------------------------------------------------------------------------------------------
  // Fast subdivision for a mesh whose verts have a magnitude of 1
  void Subdivide(std::vector<aiVector3D>& positions)
  {
      // assume this to be constant - (fixme: must be 1.0? I think so)
      const ai_real fl1 = positions[0].Length();
  
      unsigned int origSize = (unsigned int)positions.size();
      for (unsigned int i = 0 ; i < origSize ; i+=3)
      {
          aiVector3D& tv0 = positions[i];
          aiVector3D& tv1 = positions[i+1];
          aiVector3D& tv2 = positions[i+2];
  
          aiVector3D a = tv0, b = tv1, c = tv2;
          aiVector3D v1 = aiVector3D(a.x+b.x, a.y+b.y, a.z+b.z).Normalize()*fl1;
          aiVector3D v2 = aiVector3D(a.x+c.x, a.y+c.y, a.z+c.z).Normalize()*fl1;
          aiVector3D v3 = aiVector3D(b.x+c.x, b.y+c.y, b.z+c.z).Normalize()*fl1;
  
          tv0 = v1; tv1 = v3; tv2 = v2; // overwrite the original
          ADD_TRIANGLE(v1, v2, a);
          ADD_TRIANGLE(v2, v3, c);
          ADD_TRIANGLE(v3, v1, b);
      }
  }
  
  // ------------------------------------------------------------------------------------------------
  // Construct a mesh from given vertex positions
  aiMesh* StandardShapes::MakeMesh(const std::vector<aiVector3D>& positions,
      unsigned int numIndices)
  {
      if (positions.empty() || !numIndices) return NULL;
  
      // Determine which kinds of primitives the mesh consists of
      aiMesh* out = new aiMesh();
      switch (numIndices) {
          case 1:
              out->mPrimitiveTypes = aiPrimitiveType_POINT;
              break;
          case 2:
              out->mPrimitiveTypes = aiPrimitiveType_LINE;
              break;
          case 3:
              out->mPrimitiveTypes = aiPrimitiveType_TRIANGLE;
              break;
          default:
              out->mPrimitiveTypes = aiPrimitiveType_POLYGON;
              break;
      };
  
      out->mNumFaces = (unsigned int)positions.size() / numIndices;
      out->mFaces = new aiFace[out->mNumFaces];
      for (unsigned int i = 0, a = 0; i < out->mNumFaces;++i) {
          aiFace& f = out->mFaces[i];
          f.mNumIndices = numIndices;
          f.mIndices = new unsigned int[numIndices];
          for (unsigned int j = 0; i < numIndices; ++i, ++a) {
              f.mIndices[j] = a;
          }
      }
      out->mNumVertices = (unsigned int)positions.size();
      out->mVertices = new aiVector3D[out->mNumVertices];
      ::memcpy(out->mVertices,&positions[0],out->mNumVertices*sizeof(aiVector3D));
  
      return out;
  }
  
  // ------------------------------------------------------------------------------------------------
  // Construct a mesh with a specific shape (callback)
  aiMesh* StandardShapes::MakeMesh ( unsigned int (*GenerateFunc)(
      std::vector<aiVector3D>&))
  {
      std::vector<aiVector3D> temp;
      unsigned num = (*GenerateFunc)(temp);
      return MakeMesh(temp,num);
  }
  
  // ------------------------------------------------------------------------------------------------
  // Construct a mesh with a specific shape (callback)
  aiMesh* StandardShapes::MakeMesh ( unsigned int (*GenerateFunc)(
      std::vector<aiVector3D>&, bool))
  {
      std::vector<aiVector3D> temp;
      unsigned num = (*GenerateFunc)(temp,true);
      return MakeMesh(temp,num);
  }
  
  // ------------------------------------------------------------------------------------------------
  // Construct a mesh with a specific shape (callback)
  aiMesh* StandardShapes::MakeMesh (unsigned int num,  void (*GenerateFunc)(
      unsigned int,std::vector<aiVector3D>&))
  {
      std::vector<aiVector3D> temp;
      (*GenerateFunc)(num,temp);
      return MakeMesh(temp,3);
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build an incosahedron with points.magnitude == 1
  unsigned int StandardShapes::MakeIcosahedron(std::vector<aiVector3D>& positions)
  {
      positions.reserve(positions.size()+60);
  
      const ai_real t = ( ai_real( 1.0 )+ ai_real( 2.236067977 ) ) / ai_real( 2.0 );
      const ai_real s = std::sqrt(ai_real(1.0) + t*t);
  
      const aiVector3D v0  = aiVector3D(t,1.0, 0.0)/s;
      const aiVector3D v1  = aiVector3D(-t,1.0, 0.0)/s;
      const aiVector3D v2  = aiVector3D(t,-1.0, 0.0)/s;
      const aiVector3D v3  = aiVector3D(-t,-1.0, 0.0)/s;
      const aiVector3D v4  = aiVector3D(1.0, 0.0, t)/s;
      const aiVector3D v5  = aiVector3D(1.0, 0.0,-t)/s;
      const aiVector3D v6  = aiVector3D(-1.0, 0.0,t)/s;
      const aiVector3D v7  = aiVector3D(-1.0, 0.0,-t)/s;
      const aiVector3D v8  = aiVector3D(0.0, t, 1.0)/s;
      const aiVector3D v9  = aiVector3D(0.0,-t, 1.0)/s;
      const aiVector3D v10 = aiVector3D(0.0, t,-1.0)/s;
      const aiVector3D v11 = aiVector3D(0.0,-t,-1.0)/s;
  
      ADD_TRIANGLE(v0,v8,v4);
      ADD_TRIANGLE(v0,v5,v10);
      ADD_TRIANGLE(v2,v4,v9);
      ADD_TRIANGLE(v2,v11,v5);
  
      ADD_TRIANGLE(v1,v6,v8);
      ADD_TRIANGLE(v1,v10,v7);
      ADD_TRIANGLE(v3,v9,v6);
      ADD_TRIANGLE(v3,v7,v11);
  
      ADD_TRIANGLE(v0,v10,v8);
      ADD_TRIANGLE(v1,v8,v10);
      ADD_TRIANGLE(v2,v9,v11);
      ADD_TRIANGLE(v3,v11,v9);
  
      ADD_TRIANGLE(v4,v2,v0);
      ADD_TRIANGLE(v5,v0,v2);
      ADD_TRIANGLE(v6,v1,v3);
      ADD_TRIANGLE(v7,v3,v1);
  
      ADD_TRIANGLE(v8,v6,v4);
      ADD_TRIANGLE(v9,v4,v6);
      ADD_TRIANGLE(v10,v5,v7);
      ADD_TRIANGLE(v11,v7,v5);
      return 3;
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build a dodecahedron with points.magnitude == 1
  unsigned int StandardShapes::MakeDodecahedron(std::vector<aiVector3D>& positions,
      bool polygons /*= false*/)
  {
      positions.reserve(positions.size()+108);
  
      const ai_real a = ai_real( 1.0 ) / ai_real(1.7320508);
      const ai_real b = std::sqrt(( ai_real( 3.0 )- ai_real( 2.23606797))/ ai_real( 6.0) );
      const ai_real c = std::sqrt(( ai_real( 3.0 )+ ai_real( 2.23606797f))/ ai_real( 6.0) );
  
      const aiVector3D v0  = aiVector3D(a,a,a);
      const aiVector3D v1  = aiVector3D(a,a,-a);
      const aiVector3D v2  = aiVector3D(a,-a,a);
      const aiVector3D v3  = aiVector3D(a,-a,-a);
      const aiVector3D v4  = aiVector3D(-a,a,a);
      const aiVector3D v5  = aiVector3D(-a,a,-a);
      const aiVector3D v6  = aiVector3D(-a,-a,a);
      const aiVector3D v7  = aiVector3D(-a,-a,-a);
      const aiVector3D v8  = aiVector3D(b,c,0.0);
      const aiVector3D v9  = aiVector3D(-b,c,0.0);
      const aiVector3D v10 = aiVector3D(b,-c,0.0);
      const aiVector3D v11 = aiVector3D(-b,-c,0.0);
      const aiVector3D v12 = aiVector3D(c, 0.0, b);
      const aiVector3D v13 = aiVector3D(c, 0.0, -b);
      const aiVector3D v14 = aiVector3D(-c, 0.0, b);
      const aiVector3D v15 = aiVector3D(-c, 0.0, -b);
      const aiVector3D v16 = aiVector3D(0.0, b, c);
      const aiVector3D v17 = aiVector3D(0.0, -b, c);
      const aiVector3D v18 = aiVector3D(0.0, b, -c);
      const aiVector3D v19 = aiVector3D(0.0, -b, -c);
  
      ADD_PENTAGON(v0, v8, v9, v4, v16);
      ADD_PENTAGON(v0, v12, v13, v1, v8);
      ADD_PENTAGON(v0, v16, v17, v2, v12);
      ADD_PENTAGON(v8, v1, v18, v5, v9);
      ADD_PENTAGON(v12, v2, v10, v3, v13);
      ADD_PENTAGON(v16, v4, v14, v6, v17);
      ADD_PENTAGON(v9, v5, v15, v14, v4);
  
      ADD_PENTAGON(v6, v11, v10, v2, v17);
      ADD_PENTAGON(v3, v19, v18, v1, v13);
      ADD_PENTAGON(v7, v15, v5, v18, v19);
      ADD_PENTAGON(v7, v11, v6, v14, v15);
      ADD_PENTAGON(v7, v19, v3, v10, v11);
      return (polygons ? 5 : 3);
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build an octahedron with points.magnitude == 1
  unsigned int StandardShapes::MakeOctahedron(std::vector<aiVector3D>& positions)
  {
      positions.reserve(positions.size()+24);
  
      const aiVector3D v0  = aiVector3D(1.0, 0.0, 0.0) ;
      const aiVector3D v1  = aiVector3D(-1.0, 0.0, 0.0);
      const aiVector3D v2  = aiVector3D(0.0, 1.0, 0.0);
      const aiVector3D v3  = aiVector3D(0.0, -1.0, 0.0);
      const aiVector3D v4  = aiVector3D(0.0, 0.0, 1.0);
      const aiVector3D v5  = aiVector3D(0.0, 0.0, -1.0);
  
      ADD_TRIANGLE(v4,v0,v2);
      ADD_TRIANGLE(v4,v2,v1);
      ADD_TRIANGLE(v4,v1,v3);
      ADD_TRIANGLE(v4,v3,v0);
  
      ADD_TRIANGLE(v5,v2,v0);
      ADD_TRIANGLE(v5,v1,v2);
      ADD_TRIANGLE(v5,v3,v1);
      ADD_TRIANGLE(v5,v0,v3);
      return 3;
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build a tetrahedron with points.magnitude == 1
  unsigned int StandardShapes::MakeTetrahedron(std::vector<aiVector3D>& positions)
  {
      positions.reserve(positions.size()+9);
  
      const ai_real invThree = ai_real( 1.0 ) / ai_real( 3.0 );
      const ai_real a = ai_real( 1.41421 ) * invThree;
      const ai_real b = ai_real( 2.4494 ) * invThree;
  
      const aiVector3D v0  = aiVector3D(0.0,0.0,1.0);
      const aiVector3D v1  = aiVector3D(2*a,0,-invThree );
      const aiVector3D v2  = aiVector3D(-a,b,-invThree );
      const aiVector3D v3  = aiVector3D(-a,-b,-invThree );
  
      ADD_TRIANGLE(v0,v1,v2);
      ADD_TRIANGLE(v0,v2,v3);
      ADD_TRIANGLE(v0,v3,v1);
      ADD_TRIANGLE(v1,v3,v2);
      return 3;
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build a hexahedron with points.magnitude == 1
  unsigned int StandardShapes::MakeHexahedron(std::vector<aiVector3D>& positions,
      bool polygons /*= false*/)
  {
      positions.reserve(positions.size()+36);
      const ai_real length = ai_real(1.0)/ai_real(1.73205080);
  
      const aiVector3D v0  = aiVector3D(-1.0,-1.0,-1.0)*length;
      const aiVector3D v1  = aiVector3D(1.0,-1.0,-1.0)*length;
      const aiVector3D v2  = aiVector3D(1.0,1.0,-1.0)*length;
      const aiVector3D v3  = aiVector3D(-1.0,1.0,-1.0)*length;
      const aiVector3D v4  = aiVector3D(-1.0,-1.0,1.0)*length;
      const aiVector3D v5  = aiVector3D(1.0,-1.0,1.0)*length;
      const aiVector3D v6  = aiVector3D(1.0,1.0,1.0)*length;
      const aiVector3D v7  = aiVector3D(-1.0,1.0,1.0)*length;
  
      ADD_QUAD(v0,v3,v2,v1);
      ADD_QUAD(v0,v1,v5,v4);
      ADD_QUAD(v0,v4,v7,v3);
      ADD_QUAD(v6,v5,v1,v2);
      ADD_QUAD(v6,v2,v3,v7);
      ADD_QUAD(v6,v7,v4,v5);
      return (polygons ? 4 : 3);
  }
  
  // Cleanup ...
  #undef ADD_TRIANGLE
  #undef ADD_QUAD
  #undef ADD_PENTAGON
  
  // ------------------------------------------------------------------------------------------------
  // Create a subdivision sphere
  void StandardShapes::MakeSphere(unsigned int    tess,
      std::vector<aiVector3D>& positions)
  {
      // Reserve enough storage. Every subdivision
      // splits each triangle in 4, the icosahedron consists of 60 verts
      positions.reserve(positions.size()+60 * integer_pow(4, tess));
  
      // Construct an icosahedron to start with
      MakeIcosahedron(positions);
  
      // ... and subdivide it until the requested output
      // tessellation is reached
      for (unsigned int i = 0; i<tess;++i)
          Subdivide(positions);
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build a cone
  void StandardShapes::MakeCone(ai_real height,ai_real radius1,
      ai_real radius2,unsigned int tess,
      std::vector<aiVector3D>& positions,bool bOpen /*= false */)
  {
      // Sorry, a cone with less than 3 segments makes ABSOLUTELY NO SENSE
      if (tess < 3 || !height)
          return;
  
      size_t old = positions.size();
  
      // No negative radii
      radius1 = std::fabs(radius1);
      radius2 = std::fabs(radius2);
  
      ai_real halfHeight = height / ai_real(2.0);
  
      // radius1 is always the smaller one
      if (radius2 > radius1)
      {
          std::swap(radius2,radius1);
          halfHeight = -halfHeight;
      }
      else old = SIZE_MAX;
  
      // Use a large epsilon to check whether the cone is pointy
      if (radius1 < (radius2-radius1)*10e-3)radius1 = 0.0;
  
      // We will need 3*2 verts per segment + 3*2 verts per segment
      // if the cone is closed
      const unsigned int mem = tess*6 + (!bOpen ? tess*3 * (radius1 ? 2 : 1) : 0);
      positions.reserve(positions.size () + mem);
  
      // Now construct all segments
      const ai_real angle_delta = (ai_real)AI_MATH_TWO_PI / tess;
      const ai_real angle_max   = (ai_real)AI_MATH_TWO_PI;
  
      ai_real s = 1.0; // std::cos(angle == 0);
      ai_real t = 0.0; // std::sin(angle == 0);
  
      for (ai_real angle = 0.0; angle < angle_max; )
      {
          const aiVector3D v1 = aiVector3D (s * radius1, -halfHeight, t * radius1 );
          const aiVector3D v2 = aiVector3D (s * radius2,  halfHeight, t * radius2 );
  
          const ai_real next = angle + angle_delta;
          ai_real s2 = std::cos(next);
          ai_real t2 = std::sin(next);
  
          const aiVector3D v3 = aiVector3D (s2 * radius2,  halfHeight, t2 * radius2 );
          const aiVector3D v4 = aiVector3D (s2 * radius1, -halfHeight, t2 * radius1 );
  
          positions.push_back(v1);
          positions.push_back(v2);
          positions.push_back(v3);
          positions.push_back(v4);
          positions.push_back(v1);
          positions.push_back(v3);
  
          if (!bOpen)
          {
              // generate the end 'cap'
              positions.push_back(aiVector3D(s * radius2,  halfHeight, t * radius2 ));
              positions.push_back(aiVector3D(s2 * radius2,  halfHeight, t2 * radius2 ));
              positions.push_back(aiVector3D(0.0, halfHeight, 0.0));
  
  
              if (radius1)
              {
                  // generate the other end 'cap'
                  positions.push_back(aiVector3D(s * radius1,  -halfHeight, t * radius1 ));
                  positions.push_back(aiVector3D(s2 * radius1,  -halfHeight, t2 * radius1 ));
                  positions.push_back(aiVector3D(0.0, -halfHeight, 0.0));
  
              }
          }
          s = s2;
          t = t2;
          angle = next;
      }
  
      // Need to flip face order?
      if ( SIZE_MAX != old )  {
          for (size_t p = old; p < positions.size();p += 3) {
              std::swap(positions[p],positions[p+1]);
          }
      }
  }
  
  // ------------------------------------------------------------------------------------------------
  // Build a circle
  void StandardShapes::MakeCircle(ai_real radius, unsigned int tess,
      std::vector<aiVector3D>& positions)
  {
      // Sorry, a circle with less than 3 segments makes ABSOLUTELY NO SENSE
      if (tess < 3 || !radius)
          return;
  
      radius = std::fabs(radius);
  
      // We will need 3 vertices per segment
      positions.reserve(positions.size()+tess*3);
  
      const ai_real angle_delta = (ai_real)AI_MATH_TWO_PI / tess;
      const ai_real angle_max   = (ai_real)AI_MATH_TWO_PI;
  
      ai_real s = 1.0; // std::cos(angle == 0);
      ai_real t = 0.0; // std::sin(angle == 0);
  
      for (ai_real angle = 0.0; angle < angle_max;  )
      {
          positions.push_back(aiVector3D(s * radius,0.0,t * radius));
          angle += angle_delta;
          s = std::cos(angle);
          t = std::sin(angle);
          positions.push_back(aiVector3D(s * radius,0.0,t * radius));
  
          positions.push_back(aiVector3D(0.0,0.0,0.0));
      }
  }
  
  } // ! Assimp
  