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diff --git a/src/agg/agg_trans_affine.h b/src/agg/agg_trans_affine.h new file mode 100644 index 000000000..1a6116388 --- /dev/null +++ b/src/agg/agg_trans_affine.h @@ -0,0 +1,518 @@ +//---------------------------------------------------------------------------- +// 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 +//---------------------------------------------------------------------------- +// +// Affine transformation classes. +// +//---------------------------------------------------------------------------- +#ifndef AGG_TRANS_AFFINE_INCLUDED +#define AGG_TRANS_AFFINE_INCLUDED + +#include <math.h> +#include "agg_basics.h" + +namespace agg +{ + const double affine_epsilon = 1e-14; + + //============================================================trans_affine + // + // See Implementation agg_trans_affine.cpp + // + // Affine transformation are linear transformations in Cartesian coordinates + // (strictly speaking not only in Cartesian, but for the beginning we will + // think so). They are rotation, scaling, translation and skewing. + // After any affine transformation a line segment remains a line segment + // and it will never become a curve. + // + // There will be no math about matrix calculations, since it has been + // described many times. Ask yourself a very simple question: + // "why do we need to understand and use some matrix stuff instead of just + // rotating, scaling and so on". The answers are: + // + // 1. Any combination of transformations can be done by only 4 multiplications + // and 4 additions in floating point. + // 2. One matrix transformation is equivalent to the number of consecutive + // discrete transformations, i.e. the matrix "accumulates" all transformations + // in the order of their settings. Suppose we have 4 transformations: + // * rotate by 30 degrees, + // * scale X to 2.0, + // * scale Y to 1.5, + // * move to (100, 100). + // The result will depend on the order of these transformations, + // and the advantage of matrix is that the sequence of discret calls: + // rotate(30), scaleX(2.0), scaleY(1.5), move(100,100) + // will have exactly the same result as the following matrix transformations: + // + // affine_matrix m; + // m *= rotate_matrix(30); + // m *= scaleX_matrix(2.0); + // m *= scaleY_matrix(1.5); + // m *= move_matrix(100,100); + // + // m.transform_my_point_at_last(x, y); + // + // What is the good of it? In real life we will set-up the matrix only once + // and then transform many points, let alone the convenience to set any + // combination of transformations. + // + // So, how to use it? Very easy - literally as it's shown above. Not quite, + // let us write a correct example: + // + // agg::trans_affine m; + // m *= agg::trans_affine_rotation(30.0 * 3.1415926 / 180.0); + // m *= agg::trans_affine_scaling(2.0, 1.5); + // m *= agg::trans_affine_translation(100.0, 100.0); + // m.transform(&x, &y); + // + // The affine matrix is all you need to perform any linear transformation, + // but all transformations have origin point (0,0). It means that we need to + // use 2 translations if we want to rotate someting around (100,100): + // + // m *= agg::trans_affine_translation(-100.0, -100.0); // move to (0,0) + // m *= agg::trans_affine_rotation(30.0 * 3.1415926 / 180.0); // rotate + // m *= agg::trans_affine_translation(100.0, 100.0); // move back to (100,100) + //---------------------------------------------------------------------- + struct trans_affine + { + double sx, shy, shx, sy, tx, ty; + + //------------------------------------------ Construction + // Identity matrix + trans_affine() : + sx(1.0), shy(0.0), shx(0.0), sy(1.0), tx(0.0), ty(0.0) + {} + + // Custom matrix. Usually used in derived classes + trans_affine(double v0, double v1, double v2, + double v3, double v4, double v5) : + sx(v0), shy(v1), shx(v2), sy(v3), tx(v4), ty(v5) + {} + + // Custom matrix from m[6] + explicit trans_affine(const double* m) : + sx(m[0]), shy(m[1]), shx(m[2]), sy(m[3]), tx(m[4]), ty(m[5]) + {} + + // Rectangle to a parallelogram. + trans_affine(double x1, double y1, double x2, double y2, + const double* parl) + { + rect_to_parl(x1, y1, x2, y2, parl); + } + + // Parallelogram to a rectangle. + trans_affine(const double* parl, + double x1, double y1, double x2, double y2) + { + parl_to_rect(parl, x1, y1, x2, y2); + } + + // Arbitrary parallelogram transformation. + trans_affine(const double* src, const double* dst) + { + parl_to_parl(src, dst); + } + + //---------------------------------- Parellelogram transformations + // transform a parallelogram to another one. Src and dst are + // pointers to arrays of three points (double[6], x1,y1,...) that + // identify three corners of the parallelograms assuming implicit + // fourth point. The arguments are arrays of double[6] mapped + // to x1,y1, x2,y2, x3,y3 where the coordinates are: + // *-----------------* + // / (x3,y3)/ + // / / + // /(x1,y1) (x2,y2)/ + // *-----------------* + const trans_affine& parl_to_parl(const double* src, + const double* dst); + + const trans_affine& rect_to_parl(double x1, double y1, + double x2, double y2, + const double* parl); + + const trans_affine& parl_to_rect(const double* parl, + double x1, double y1, + double x2, double y2); + + + //------------------------------------------ Operations + // Reset - load an identity matrix + const trans_affine& reset(); + + // Direct transformations operations + const trans_affine& translate(double x, double y); + const trans_affine& rotate(double a); + const trans_affine& scale(double s); + const trans_affine& scale(double x, double y); + + // Multiply matrix to another one + const trans_affine& multiply(const trans_affine& m); + + // Multiply "m" to "this" and assign the result to "this" + const trans_affine& premultiply(const trans_affine& m); + + // Multiply matrix to inverse of another one + const trans_affine& multiply_inv(const trans_affine& m); + + // Multiply inverse of "m" to "this" and assign the result to "this" + const trans_affine& premultiply_inv(const trans_affine& m); + + // Invert matrix. Do not try to invert degenerate matrices, + // there's no check for validity. If you set scale to 0 and + // then try to invert matrix, expect unpredictable result. + const trans_affine& invert(); + + // Mirroring around X + const trans_affine& flip_x(); + + // Mirroring around Y + const trans_affine& flip_y(); + + //------------------------------------------- Load/Store + // Store matrix to an array [6] of double + void store_to(double* m) const + { + *m++ = sx; *m++ = shy; *m++ = shx; *m++ = sy; *m++ = tx; *m++ = ty; + } + + // Load matrix from an array [6] of double + const trans_affine& load_from(const double* m) + { + sx = *m++; shy = *m++; shx = *m++; sy = *m++; tx = *m++; ty = *m++; + return *this; + } + + //------------------------------------------- Operators + + // Multiply the matrix by another one + const trans_affine& operator *= (const trans_affine& m) + { + return multiply(m); + } + + // Multiply the matrix by inverse of another one + const trans_affine& operator /= (const trans_affine& m) + { + return multiply_inv(m); + } + + // Multiply the matrix by another one and return + // the result in a separete matrix. + trans_affine operator * (const trans_affine& m) const + { + return trans_affine(*this).multiply(m); + } + + // Multiply the matrix by inverse of another one + // and return the result in a separete matrix. + trans_affine operator / (const trans_affine& m) const + { + return trans_affine(*this).multiply_inv(m); + } + + // Calculate and return the inverse matrix + trans_affine operator ~ () const + { + trans_affine ret = *this; + return ret.invert(); + } + + // Equal operator with default epsilon + bool operator == (const trans_affine& m) const + { + return is_equal(m, affine_epsilon); + } + + // Not Equal operator with default epsilon + bool operator != (const trans_affine& 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, 2x2 matrix only, no translation + void transform_2x2(double* x, double* y) const; + + // Inverse transformation of x and y. It works slower than the + // direct transformation. For massive operations it's better to + // invert() the matrix and then use direct transformations. + void inverse_transform(double* x, double* y) const; + + //-------------------------------------------- Auxiliary + // Calculate the determinant of matrix + double determinant() const + { + return sx * sy - shy * shx; + } + + // Calculate the reciprocal of the determinant + double determinant_reciprocal() const + { + return 1.0 / (sx * sy - shy * shx); + } + + // Get the average scale (by X and Y). + // Basically used to calculate the approximation_scale when + // decomposinting curves into line segments. + double scale() const; + + // Check to see if the matrix is not degenerate + bool is_valid(double epsilon = affine_epsilon) const; + + // Check to see if it's an identity matrix + bool is_identity(double epsilon = affine_epsilon) const; + + // Check to see if two matrices are equal + bool is_equal(const trans_affine& m, double epsilon = affine_epsilon) const; + + // Determine the major parameters. Use with caution considering + // possible degenerate cases. + 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; + }; + + //------------------------------------------------------------------------ + inline void trans_affine::transform(double* x, double* y) const + { + double tmp = *x; + *x = tmp * sx + *y * shx + tx; + *y = tmp * shy + *y * sy + ty; + } + + //------------------------------------------------------------------------ + inline void trans_affine::transform_2x2(double* x, double* y) const + { + double tmp = *x; + *x = tmp * sx + *y * shx; + *y = tmp * shy + *y * sy; + } + + //------------------------------------------------------------------------ + inline void trans_affine::inverse_transform(double* x, double* y) const + { + double d = determinant_reciprocal(); + double a = (*x - tx) * d; + double b = (*y - ty) * d; + *x = a * sy - b * shx; + *y = b * sx - a * shy; + } + + //------------------------------------------------------------------------ + inline double trans_affine::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 const trans_affine& trans_affine::translate(double x, double y) + { + tx += x; + ty += y; + return *this; + } + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::rotate(double a) + { + double ca = cos(a); + double sa = sin(a); + double t0 = sx * ca - shy * sa; + double t2 = shx * ca - sy * sa; + double t4 = tx * ca - ty * sa; + shy = sx * sa + shy * ca; + sy = shx * sa + sy * ca; + ty = tx * sa + ty * ca; + sx = t0; + shx = t2; + tx = t4; + return *this; + } + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::scale(double x, double y) + { + double mm0 = x; // Possible hint for the optimizer + double mm3 = y; + sx *= mm0; + shx *= mm0; + tx *= mm0; + shy *= mm3; + sy *= mm3; + ty *= mm3; + return *this; + } + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::scale(double s) + { + double m = s; // Possible hint for the optimizer + sx *= m; + shx *= m; + tx *= m; + shy *= m; + sy *= m; + ty *= m; + return *this; + } + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::premultiply(const trans_affine& m) + { + trans_affine t = m; + return *this = t.multiply(*this); + } + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::multiply_inv(const trans_affine& m) + { + trans_affine t = m; + t.invert(); + return multiply(t); + } + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::premultiply_inv(const trans_affine& m) + { + trans_affine t = m; + t.invert(); + return *this = t.multiply(*this); + } + + //------------------------------------------------------------------------ + inline void trans_affine::scaling_abs(double* x, double* y) const + { + // Used to calculate scaling coefficients in image resampling. + // When there is considerable shear this method gives us much + // better estimation than just sx, sy. + *x = sqrt(sx * sx + shx * shx); + *y = sqrt(shy * shy + sy * sy); + } + + //====================================================trans_affine_rotation + // Rotation matrix. sin() and cos() are calculated twice for the same angle. + // There's no harm because the performance of sin()/cos() is very good on all + // modern processors. Besides, this operation is not going to be invoked too + // often. + class trans_affine_rotation : public trans_affine + { + public: + trans_affine_rotation(double a) : + trans_affine(cos(a), sin(a), -sin(a), cos(a), 0.0, 0.0) + {} + }; + + //====================================================trans_affine_scaling + // Scaling matrix. x, y - scale coefficients by X and Y respectively + class trans_affine_scaling : public trans_affine + { + public: + trans_affine_scaling(double x, double y) : + trans_affine(x, 0.0, 0.0, y, 0.0, 0.0) + {} + + trans_affine_scaling(double s) : + trans_affine(s, 0.0, 0.0, s, 0.0, 0.0) + {} + }; + + //================================================trans_affine_translation + // Translation matrix + class trans_affine_translation : public trans_affine + { + public: + trans_affine_translation(double x, double y) : + trans_affine(1.0, 0.0, 0.0, 1.0, x, y) + {} + }; + + //====================================================trans_affine_skewing + // Sckewing (shear) matrix + class trans_affine_skewing : public trans_affine + { + public: + trans_affine_skewing(double x, double y) : + trans_affine(1.0, tan(y), tan(x), 1.0, 0.0, 0.0) + {} + }; + + + //===============================================trans_affine_line_segment + // Rotate, Scale and Translate, associating 0...dist with line segment + // x1,y1,x2,y2 + class trans_affine_line_segment : public trans_affine + { + public: + trans_affine_line_segment(double x1, double y1, double x2, double y2, + double dist) + { + double dx = x2 - x1; + double dy = y2 - y1; + if(dist > 0.0) + { + multiply(trans_affine_scaling(sqrt(dx * dx + dy * dy) / dist)); + } + multiply(trans_affine_rotation(atan2(dy, dx))); + multiply(trans_affine_translation(x1, y1)); + } + }; + + + //============================================trans_affine_reflection_unit + // Reflection matrix. Reflect coordinates across the line through + // the origin containing the unit vector (ux, uy). + // Contributed by John Horigan + class trans_affine_reflection_unit : public trans_affine + { + public: + trans_affine_reflection_unit(double ux, double uy) : + trans_affine(2.0 * ux * ux - 1.0, + 2.0 * ux * uy, + 2.0 * ux * uy, + 2.0 * uy * uy - 1.0, + 0.0, 0.0) + {} + }; + + + //=================================================trans_affine_reflection + // Reflection matrix. Reflect coordinates across the line through + // the origin at the angle a or containing the non-unit vector (x, y). + // Contributed by John Horigan + class trans_affine_reflection : public trans_affine_reflection_unit + { + public: + trans_affine_reflection(double a) : + trans_affine_reflection_unit(cos(a), sin(a)) + {} + + + trans_affine_reflection(double x, double y) : + trans_affine_reflection_unit(x / sqrt(x * x + y * y), y / sqrt(x * x + y * y)) + {} + }; + +} + + +#endif + |