Get 3d Vector Projection 2d Plane Code Example

Example: 3d projection onto 2d plane algorithm

#include <vector> #include <cmath> #include <stdexcept> #include <algorithm>  struct Vector {     Vector() : x(0),y(0),z(0),w(1){}     Vector(float a, float b, float c) : x(a),y(b),z(c),w(1){}      /* Assume proper operator overloads here, with vectors and scalars */     float Length() const     {         return std::sqrt(x*x + y*y + z*z);     }          Vector Unit() const     {         const float epsilon = 1e-6;         float mag = Length();         if(mag < epsilon){             std::out_of_range e("");             throw e;         }         return *this / mag;     } };  inline float Dot(const Vector& v1, const Vector& v2) {     return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; }  class Matrix {     public:     Matrix() : data(16)     {         Identity();     }     void Identity()     {         std::fill(data.begin(), data.end(), float(0));         data[0] = data[5] = data[10] = data[15] = 1.0f;     }     float& operator[](size_t index)     {         if(index >= 16){             std::out_of_range e("");             throw e;         }         return data[index];     }     Matrix operator*(const Matrix& m) const     {         Matrix dst;         int col;         for(int y=0; y<4; ++y){             col = y*4;             for(int x=0; x<4; ++x){                 for(int i=0; i<4; ++i){                     dst[x+col] += m[i+col]*data[x+i*4];                 }             }         }         return dst;     }     Matrix& operator*=(const Matrix& m)     {         *this = (*this) * m;         return *this;     }      /* The interesting stuff */     void SetupClipMatrix(float fov, float aspectRatio, float near, float far)     {         Identity();         float f = 1.0f / std::tan(fov * 0.5f);         data[0] = f*aspectRatio;         data[5] = f;         data[10] = (far+near) / (far-near);         data[11] = 1.0f; /* this 'plugs' the old z into w */         data[14] = (2.0f*near*far) / (near-far);         data[15] = 0.0f;     }      std::vector<float> data; };  inline Vector operator*(const Vector& v, const Matrix& m) {     Vector dst;     dst.x = v.x*m[0] + v.y*m[4] + v.z*m[8 ] + v.w*m[12];     dst.y = v.x*m[1] + v.y*m[5] + v.z*m[9 ] + v.w*m[13];     dst.z = v.x*m[2] + v.y*m[6] + v.z*m[10] + v.w*m[14];     dst.w = v.x*m[3] + v.y*m[7] + v.z*m[11] + v.w*m[15];     return dst; }  typedef std::vector<Vector> VecArr; VecArr ProjectAndClip(int width, int height, float near, float far, const VecArr& vertex) {     float halfWidth = (float)width * 0.5f;     float halfHeight = (float)height * 0.5f;     float aspect = (float)width / (float)height;     Vector v;     Matrix clipMatrix;     VecArr dst;     clipMatrix.SetupClipMatrix(60.0f * (M_PI / 180.0f), aspect, near, far);     /*  Here, after the perspective divide, you perform Sutherland-Hodgeman clipping          by checking if the x, y and z components are inside the range of [-w, w].         One checks each vector component seperately against each plane. Per-vertex         data like colours, normals and texture coordinates need to be linearly         interpolated for clipped edges to reflect the change. If the edge (v0,v1)         is tested against the positive x plane, and v1 is outside, the interpolant         becomes: (v1.x - w) / (v1.x - v0.x)         I skip this stage all together to be brief.     */     for(VecArr::iterator i=vertex.begin(); i!=vertex.end(); ++i){         v = (*i) * clipMatrix;         v /= v.w; /* Don't get confused here. I assume the divide leaves v.w alone.*/         dst.push_back(v);     }      /* TODO: Clipping here */      for(VecArr::iterator i=dst.begin(); i!=dst.end(); ++i){         i->x = (i->x * (float)width) / (2.0f * i->w) + halfWidth;         i->y = (i->y * (float)height) / (2.0f * i->w) + halfHeight;     }     return dst; }