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Diffstat (limited to 'agg/inc/agg_trans_affine.h')
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diff --git a/agg/inc/agg_trans_affine.h b/agg/inc/agg_trans_affine.h new file mode 100755 index 000000000000..5a4098f904de --- /dev/null +++ b/agg/inc/agg_trans_affine.h @@ -0,0 +1,344 @@ +//---------------------------------------------------------------------------- +// Anti-Grain Geometry - Version 2.3 +// 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; // About of precision of doubles + + //============================================================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) + //---------------------------------------------------------------------- + class trans_affine + { + public: + //------------------------------------------ Construction + // Construct an identity matrix - it does not transform anything + trans_affine() : + m0(1.0), m1(0.0), m2(0.0), m3(1.0), m4(0.0), m5(0.0) + {} + + // Construct a custom matrix. Usually used in derived classes + trans_affine(double v0, double v1, double v2, double v3, double v4, double v5) : + m0(v0), m1(v1), m2(v2), m3(v3), m4(v4), m5(v5) + {} + + // Construct a matrix to transform a parallelogram to another one. + trans_affine(const double* rect, const double* parl) + { + parl_to_parl(rect, parl); + } + + // Construct a matrix to transform a 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); + } + + // Construct a matrix to transform a 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); + } + + + //---------------------------------- Parellelogram transformations + // Calculate a matrix to transform a parallelogram to another one. + // src and dst are pointers to arrays of three points + // (double[6], x,y,...) that identify three corners of the + // parallelograms assuming implicit fourth points. + // There are also transformations rectangtle to parallelogram and + // parellelogram to rectangle + 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 - actually load an identity matrix + const trans_affine& reset(); + + // 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); + + // 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++ = m0; *m++ = m1; *m++ = m2; *m++ = m3; *m++ = m4; *m++ = m5; + } + + // Load matrix from an array [6] of double + const trans_affine& load_from(const double* m) + { + m0 = *m++; m1 = *m++; m2 = *m++; m3 = *m++; m4 = *m++; m5 = *m++; + return *this; + } + + //------------------------------------------- Operators + + // Multiply current matrix to another one + const trans_affine& operator *= (const trans_affine& m) + { + return multiply(m); + } + + // Multiply current matrix to another one and return + // the result in a separete matrix. + trans_affine operator * (const trans_affine& m) + { + return trans_affine(*this).multiply(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 x and y + void transform(double* x, double* y) const; + + // Inverse transformation x and y. It works slower than the + // direct transformation, so if the performance is critical + // it's better to invert() the matrix and then use transform() + void inverse_transform(double* x, double* y) const; + + //-------------------------------------------- Auxiliary + // Calculate the determinant of matrix + double determinant() const + { + return 1.0 / (m0 * m3 - m1 * m2); + } + + // 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 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 carefully considering degenerate matrices + double rotation() const; + void translation(double* dx, double* dy) const; + void scaling(double* sx, double* sy) const; + void scaling_abs(double* sx, double* sy) const + { + *sx = sqrt(m0*m0 + m2*m2); + *sy = sqrt(m1*m1 + m3*m3); + } + + private: + double m0; + double m1; + double m2; + double m3; + double m4; + double m5; + }; + + //------------------------------------------------------------------------ + inline void trans_affine::transform(double* x, double* y) const + { + register double tx = *x; + *x = tx * m0 + *y * m2 + m4; + *y = tx * m1 + *y * m3 + m5; + } + + //------------------------------------------------------------------------ + inline void trans_affine::inverse_transform(double* x, double* y) const + { + register double d = determinant(); + register double a = (*x - m4) * d; + register double b = (*y - m5) * d; + *x = a * m3 - b * m2; + *y = b * m0 - a * m1; + } + + //------------------------------------------------------------------------ + inline double trans_affine::scale() const + { + double x = 0.707106781 * m0 + 0.707106781 * m2; + double y = 0.707106781 * m1 + 0.707106781 * m3; + return sqrt(x*x + y*y); + } + + + //------------------------------------------------------------------------ + inline const trans_affine& trans_affine::premultiply(const trans_affine& m) + { + trans_affine t = m; + return *this = t.multiply(*this); + } + + + //====================================================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. sx, sy - scale coefficients by X and Y respectively + class trans_affine_scaling : public trans_affine + { + public: + trans_affine_scaling(double sx, double sy) : + trans_affine(sx, 0.0, 0.0, sy, 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 tx, double ty) : + trans_affine(1.0, 0.0, 0.0, 1.0, tx, ty) + {} + }; + + //====================================================trans_affine_skewing + // Sckewing (shear) matrix + class trans_affine_skewing : public trans_affine + { + public: + trans_affine_skewing(double sx, double sy) : + trans_affine(1.0, tan(sy), tan(sx), 1.0, 0.0, 0.0) + {} + }; + + + +} + + +#endif + |