//---------------------------------------------------------------------------- // Anti-Grain Geometry - Version 2.4 // Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com) // // Permission to copy, use, modify, sell and distribute this software // is granted provided this copyright notice appears in all copies. // This software is provided "as is" without express or implied // warranty, and with no claim as to its suitability for any purpose. // //---------------------------------------------------------------------------- // Contact: mcseem@antigrain.com // mcseemagg@yahoo.com // http://www.antigrain.com //---------------------------------------------------------------------------- // // Perspective 2D transformations // //---------------------------------------------------------------------------- #ifndef AGG_TRANS_PERSPECTIVE_INCLUDED #define AGG_TRANS_PERSPECTIVE_INCLUDED #include "agg_trans_affine.h" namespace agg { //=======================================================trans_perspective struct trans_perspective { double sx, shy, w0, shx, sy, w1, tx, ty, w2; //------------------------------------------------------- Construction // Identity matrix trans_perspective() : sx (1), shy(0), w0(0), shx(0), sy (1), w1(0), tx (0), ty (0), w2(1) {} // Custom matrix trans_perspective(double v0, double v1, double v2, double v3, double v4, double v5, double v6, double v7, double v8) : sx (v0), shy(v1), w0(v2), shx(v3), sy (v4), w1(v5), tx (v6), ty (v7), w2(v8) {} // Custom matrix from m[9] explicit trans_perspective(const double* m) : sx (m[0]), shy(m[1]), w0(m[2]), shx(m[3]), sy (m[4]), w1(m[5]), tx (m[6]), ty (m[7]), w2(m[8]) {} // From affine explicit trans_perspective(const trans_affine& a) : sx (a.sx ), shy(a.shy), w0(0), shx(a.shx), sy (a.sy ), w1(0), tx (a.tx ), ty (a.ty ), w2(1) {} // Rectangle to quadrilateral trans_perspective(double x1, double y1, double x2, double y2, const double* quad); // Quadrilateral to rectangle trans_perspective(const double* quad, double x1, double y1, double x2, double y2); // Arbitrary quadrilateral transformations trans_perspective(const double* src, const double* dst); //-------------------------------------- Quadrilateral transformations // The arguments are double[8] that are mapped to quadrilaterals: // x1,y1, x2,y2, x3,y3, x4,y4 bool quad_to_quad(const double* qs, const double* qd); bool rect_to_quad(double x1, double y1, double x2, double y2, const double* q); bool quad_to_rect(const double* q, double x1, double y1, double x2, double y2); // Map square (0,0,1,1) to the quadrilateral and vice versa bool square_to_quad(const double* q); bool quad_to_square(const double* q); //--------------------------------------------------------- Operations // Reset - load an identity matrix const trans_perspective& reset(); // Invert matrix. Returns false in degenerate case bool invert(); // Direct transformations operations const trans_perspective& translate(double x, double y); const trans_perspective& rotate(double a); const trans_perspective& scale(double s); const trans_perspective& scale(double x, double y); // Multiply the matrix by another one const trans_perspective& multiply(const trans_perspective& m); // Multiply "m" by "this" and assign the result to "this" const trans_perspective& premultiply(const trans_perspective& m); // Multiply matrix to inverse of another one const trans_perspective& multiply_inv(const trans_perspective& m); // Multiply inverse of "m" by "this" and assign the result to "this" const trans_perspective& premultiply_inv(const trans_perspective& m); // Multiply the matrix by another one const trans_perspective& multiply(const trans_affine& m); // Multiply "m" by "this" and assign the result to "this" const trans_perspective& premultiply(const trans_affine& m); // Multiply the matrix by inverse of another one const trans_perspective& multiply_inv(const trans_affine& m); // Multiply inverse of "m" by "this" and assign the result to "this" const trans_perspective& premultiply_inv(const trans_affine& m); //--------------------------------------------------------- Load/Store void store_to(double* m) const; const trans_perspective& load_from(const double* m); //---------------------------------------------------------- Operators // Multiply the matrix by another one const trans_perspective& operator *= (const trans_perspective& m) { return multiply(m); } const trans_perspective& operator *= (const trans_affine& m) { return multiply(m); } // Multiply the matrix by inverse of another one const trans_perspective& operator /= (const trans_perspective& m) { return multiply_inv(m); } const trans_perspective& operator /= (const trans_affine& m) { return multiply_inv(m); } // Multiply the matrix by another one and return // the result in a separete matrix. trans_perspective operator * (const trans_perspective& m) { return trans_perspective(*this).multiply(m); } trans_perspective operator * (const trans_affine& m) { return trans_perspective(*this).multiply(m); } // Multiply the matrix by inverse of another one // and return the result in a separete matrix. trans_perspective operator / (const trans_perspective& m) { return trans_perspective(*this).multiply_inv(m); } trans_perspective operator / (const trans_affine& m) { return trans_perspective(*this).multiply_inv(m); } // Calculate and return the inverse matrix trans_perspective operator ~ () const { trans_perspective ret = *this; ret.invert(); return ret; } // Equal operator with default epsilon bool operator == (const trans_perspective& m) const { return is_equal(m, affine_epsilon); } // Not Equal operator with default epsilon bool operator != (const trans_perspective& m) const { return !is_equal(m, affine_epsilon); } //---------------------------------------------------- Transformations // Direct transformation of x and y void transform(double* x, double* y) const; // Direct transformation of x and y, affine part only void transform_affine(double* x, double* y) const; // Direct transformation of x and y, 2x2 matrix only, no translation void transform_2x2(double* x, double* y) const; // Inverse transformation of x and y. It works slow because // it explicitly inverts the matrix on every call. For massive // operations it's better to invert() the matrix and then use // direct transformations. void inverse_transform(double* x, double* y) const; //---------------------------------------------------------- Auxiliary const trans_perspective& from_affine(const trans_affine& a); double determinant() const; double determinant_reciprocal() const; bool is_valid(double epsilon = affine_epsilon) const; bool is_identity(double epsilon = affine_epsilon) const; bool is_equal(const trans_perspective& m, double epsilon = affine_epsilon) const; // Determine the major affine parameters. Use with caution // considering possible degenerate cases. double scale() const; double rotation() const; void translation(double* dx, double* dy) const; void scaling(double* x, double* y) const; void scaling_abs(double* x, double* y) const; //-------------------------------------------------------------------- class iterator_x { double den; double den_step; double nom_x; double nom_x_step; double nom_y; double nom_y_step; public: double x; double y; iterator_x() {} iterator_x(double px, double py, double step, const trans_perspective& m) : den(px * m.w0 + py * m.w1 + m.w2), den_step(m.w0 * step), nom_x(px * m.sx + py * m.shx + m.tx), nom_x_step(step * m.sx), nom_y(px * m.shy + py * m.sy + m.ty), nom_y_step(step * m.shy), x(nom_x / den), y(nom_y / den) {} void operator ++ () { den += den_step; nom_x += nom_x_step; nom_y += nom_y_step; double d = 1.0 / den; x = nom_x * d; y = nom_y * d; } }; //-------------------------------------------------------------------- iterator_x begin(double x, double y, double step) const { return iterator_x(x, y, step, *this); } }; //------------------------------------------------------------------------ inline bool trans_perspective::square_to_quad(const double* q) { double dx = q[0] - q[2] + q[4] - q[6]; double dy = q[1] - q[3] + q[5] - q[7]; if(dx == 0.0 && dy == 0.0) { // Affine case (parallelogram) //--------------- sx = q[2] - q[0]; shy = q[3] - q[1]; w0 = 0.0; shx = q[4] - q[2]; sy = q[5] - q[3]; w1 = 0.0; tx = q[0]; ty = q[1]; w2 = 1.0; } else { double dx1 = q[2] - q[4]; double dy1 = q[3] - q[5]; double dx2 = q[6] - q[4]; double dy2 = q[7] - q[5]; double den = dx1 * dy2 - dx2 * dy1; if(den == 0.0) { // Singular case //--------------- sx = shy = w0 = shx = sy = w1 = tx = ty = w2 = 0.0; return false; } // General case //--------------- double u = (dx * dy2 - dy * dx2) / den; double v = (dy * dx1 - dx * dy1) / den; sx = q[2] - q[0] + u * q[2]; shy = q[3] - q[1] + u * q[3]; w0 = u; shx = q[6] - q[0] + v * q[6]; sy = q[7] - q[1] + v * q[7]; w1 = v; tx = q[0]; ty = q[1]; w2 = 1.0; } return true; } //------------------------------------------------------------------------ inline bool trans_perspective::invert() { double d0 = sy * w2 - w1 * ty; double d1 = w0 * ty - shy * w2; double d2 = shy * w1 - w0 * sy; double d = sx * d0 + shx * d1 + tx * d2; if(d == 0.0) { sx = shy = w0 = shx = sy = w1 = tx = ty = w2 = 0.0; return false; } d = 1.0 / d; trans_perspective a = *this; sx = d * d0; shy = d * d1; w0 = d * d2; shx = d * (a.w1 *a.tx - a.shx*a.w2); sy = d * (a.sx *a.w2 - a.w0 *a.tx); w1 = d * (a.w0 *a.shx - a.sx *a.w1); tx = d * (a.shx*a.ty - a.sy *a.tx); ty = d * (a.shy*a.tx - a.sx *a.ty); w2 = d * (a.sx *a.sy - a.shy*a.shx); return true; } //------------------------------------------------------------------------ inline bool trans_perspective::quad_to_square(const double* q) { if(!square_to_quad(q)) return false; invert(); return true; } //------------------------------------------------------------------------ inline bool trans_perspective::quad_to_quad(const double* qs, const double* qd) { trans_perspective p; if(! quad_to_square(qs)) return false; if(!p.square_to_quad(qd)) return false; multiply(p); return true; } //------------------------------------------------------------------------ inline bool trans_perspective::rect_to_quad(double x1, double y1, double x2, double y2, const double* q) { double r[8]; r[0] = r[6] = x1; r[2] = r[4] = x2; r[1] = r[3] = y1; r[5] = r[7] = y2; return quad_to_quad(r, q); } //------------------------------------------------------------------------ inline bool trans_perspective::quad_to_rect(const double* q, double x1, double y1, double x2, double y2) { double r[8]; r[0] = r[6] = x1; r[2] = r[4] = x2; r[1] = r[3] = y1; r[5] = r[7] = y2; return quad_to_quad(q, r); } //------------------------------------------------------------------------ inline trans_perspective::trans_perspective(double x1, double y1, double x2, double y2, const double* quad) { rect_to_quad(x1, y1, x2, y2, quad); } //------------------------------------------------------------------------ inline trans_perspective::trans_perspective(const double* quad, double x1, double y1, double x2, double y2) { quad_to_rect(quad, x1, y1, x2, y2); } //------------------------------------------------------------------------ inline trans_perspective::trans_perspective(const double* src, const double* dst) { quad_to_quad(src, dst); } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::reset() { sx = 1; shy = 0; w0 = 0; shx = 0; sy = 1; w1 = 0; tx = 0; ty = 0; w2 = 1; return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::multiply(const trans_perspective& a) { trans_perspective b = *this; sx = a.sx *b.sx + a.shx*b.shy + a.tx*b.w0; shx = a.sx *b.shx + a.shx*b.sy + a.tx*b.w1; tx = a.sx *b.tx + a.shx*b.ty + a.tx*b.w2; shy = a.shy*b.sx + a.sy *b.shy + a.ty*b.w0; sy = a.shy*b.shx + a.sy *b.sy + a.ty*b.w1; ty = a.shy*b.tx + a.sy *b.ty + a.ty*b.w2; w0 = a.w0 *b.sx + a.w1 *b.shy + a.w2*b.w0; w1 = a.w0 *b.shx + a.w1 *b.sy + a.w2*b.w1; w2 = a.w0 *b.tx + a.w1 *b.ty + a.w2*b.w2; return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::multiply(const trans_affine& a) { trans_perspective b = *this; sx = a.sx *b.sx + a.shx*b.shy + a.tx*b.w0; shx = a.sx *b.shx + a.shx*b.sy + a.tx*b.w1; tx = a.sx *b.tx + a.shx*b.ty + a.tx*b.w2; shy = a.shy*b.sx + a.sy *b.shy + a.ty*b.w0; sy = a.shy*b.shx + a.sy *b.sy + a.ty*b.w1; ty = a.shy*b.tx + a.sy *b.ty + a.ty*b.w2; return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::premultiply(const trans_perspective& b) { trans_perspective a = *this; sx = a.sx *b.sx + a.shx*b.shy + a.tx*b.w0; shx = a.sx *b.shx + a.shx*b.sy + a.tx*b.w1; tx = a.sx *b.tx + a.shx*b.ty + a.tx*b.w2; shy = a.shy*b.sx + a.sy *b.shy + a.ty*b.w0; sy = a.shy*b.shx + a.sy *b.sy + a.ty*b.w1; ty = a.shy*b.tx + a.sy *b.ty + a.ty*b.w2; w0 = a.w0 *b.sx + a.w1 *b.shy + a.w2*b.w0; w1 = a.w0 *b.shx + a.w1 *b.sy + a.w2*b.w1; w2 = a.w0 *b.tx + a.w1 *b.ty + a.w2*b.w2; return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::premultiply(const trans_affine& b) { trans_perspective a = *this; sx = a.sx *b.sx + a.shx*b.shy; shx = a.sx *b.shx + a.shx*b.sy; tx = a.sx *b.tx + a.shx*b.ty + a.tx; shy = a.shy*b.sx + a.sy *b.shy; sy = a.shy*b.shx + a.sy *b.sy; ty = a.shy*b.tx + a.sy *b.ty + a.ty; w0 = a.w0 *b.sx + a.w1 *b.shy; w1 = a.w0 *b.shx + a.w1 *b.sy; w2 = a.w0 *b.tx + a.w1 *b.ty + a.w2; return *this; } //------------------------------------------------------------------------ const trans_perspective& trans_perspective::multiply_inv(const trans_perspective& m) { trans_perspective t = m; t.invert(); return multiply(t); } //------------------------------------------------------------------------ const trans_perspective& trans_perspective::multiply_inv(const trans_affine& m) { trans_affine t = m; t.invert(); return multiply(t); } //------------------------------------------------------------------------ const trans_perspective& trans_perspective::premultiply_inv(const trans_perspective& m) { trans_perspective t = m; t.invert(); return *this = t.multiply(*this); } //------------------------------------------------------------------------ const trans_perspective& trans_perspective::premultiply_inv(const trans_affine& m) { trans_perspective t(m); t.invert(); return *this = t.multiply(*this); } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::translate(double x, double y) { tx += x; ty += y; return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::rotate(double a) { multiply(trans_affine_rotation(a)); return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::scale(double s) { multiply(trans_affine_scaling(s)); return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::scale(double x, double y) { multiply(trans_affine_scaling(x, y)); return *this; } //------------------------------------------------------------------------ inline void trans_perspective::transform(double* px, double* py) const { double x = *px; double y = *py; double m = 1.0 / (x*w0 + y*w1 + w2); *px = m * (x*sx + y*shx + tx); *py = m * (x*shy + y*sy + ty); } //------------------------------------------------------------------------ inline void trans_perspective::transform_affine(double* x, double* y) const { double tmp = *x; *x = tmp * sx + *y * shx + tx; *y = tmp * shy + *y * sy + ty; } //------------------------------------------------------------------------ inline void trans_perspective::transform_2x2(double* x, double* y) const { double tmp = *x; *x = tmp * sx + *y * shx; *y = tmp * shy + *y * sy; } //------------------------------------------------------------------------ inline void trans_perspective::inverse_transform(double* x, double* y) const { trans_perspective t(*this); if(t.invert()) t.transform(x, y); } //------------------------------------------------------------------------ inline void trans_perspective::store_to(double* m) const { *m++ = sx; *m++ = shy; *m++ = w0; *m++ = shx; *m++ = sy; *m++ = w1; *m++ = tx; *m++ = ty; *m++ = w2; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::load_from(const double* m) { sx = *m++; shy = *m++; w0 = *m++; shx = *m++; sy = *m++; w1 = *m++; tx = *m++; ty = *m++; w2 = *m++; return *this; } //------------------------------------------------------------------------ inline const trans_perspective& trans_perspective::from_affine(const trans_affine& a) { sx = a.sx; shy = a.shy; w0 = 0; shx = a.shx; sy = a.sy; w1 = 0; tx = a.tx; ty = a.ty; w2 = 1; return *this; } //------------------------------------------------------------------------ inline double trans_perspective::determinant() const { return sx * (sy * w2 - ty * w1) + shx * (ty * w0 - shy * w2) + tx * (shy * w1 - sy * w0); } //------------------------------------------------------------------------ inline double trans_perspective::determinant_reciprocal() const { return 1.0 / determinant(); } //------------------------------------------------------------------------ inline bool trans_perspective::is_valid(double epsilon) const { return std::fabs(sx) > epsilon && std::fabs(sy) > epsilon && std::fabs(w2) > epsilon; } //------------------------------------------------------------------------ inline bool trans_perspective::is_identity(double epsilon) const { return is_equal_eps(sx, 1.0, epsilon) && is_equal_eps(shy, 0.0, epsilon) && is_equal_eps(w0, 0.0, epsilon) && is_equal_eps(shx, 0.0, epsilon) && is_equal_eps(sy, 1.0, epsilon) && is_equal_eps(w1, 0.0, epsilon) && is_equal_eps(tx, 0.0, epsilon) && is_equal_eps(ty, 0.0, epsilon) && is_equal_eps(w2, 1.0, epsilon); } //------------------------------------------------------------------------ inline bool trans_perspective::is_equal(const trans_perspective& m, double epsilon) const { return is_equal_eps(sx, m.sx, epsilon) && is_equal_eps(shy, m.shy, epsilon) && is_equal_eps(w0, m.w0, epsilon) && is_equal_eps(shx, m.shx, epsilon) && is_equal_eps(sy, m.sy, epsilon) && is_equal_eps(w1, m.w1, epsilon) && is_equal_eps(tx, m.tx, epsilon) && is_equal_eps(ty, m.ty, epsilon) && is_equal_eps(w2, m.w2, epsilon); } //------------------------------------------------------------------------ inline double trans_perspective::scale() const { double x = 0.707106781 * sx + 0.707106781 * shx; double y = 0.707106781 * shy + 0.707106781 * sy; return sqrt(x*x + y*y); } //------------------------------------------------------------------------ inline double trans_perspective::rotation() const { double x1 = 0.0; double y1 = 0.0; double x2 = 1.0; double y2 = 0.0; transform(&x1, &y1); transform(&x2, &y2); return std::atan2(y2-y1, x2-x1); } //------------------------------------------------------------------------ void trans_perspective::translation(double* dx, double* dy) const { *dx = tx; *dy = ty; } //------------------------------------------------------------------------ void trans_perspective::scaling(double* x, double* y) const { double x1 = 0.0; double y1 = 0.0; double x2 = 1.0; double y2 = 1.0; trans_perspective t(*this); t *= trans_affine_rotation(-rotation()); t.transform(&x1, &y1); t.transform(&x2, &y2); *x = x2 - x1; *y = y2 - y1; } //------------------------------------------------------------------------ void trans_perspective::scaling_abs(double* x, double* y) const { *x = sqrt(sx * sx + shx * shx); *y = sqrt(shy * shy + sy * sy); } } #endif