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519 lines
18 KiB
C++
519 lines
18 KiB
C++
//----------------------------------------------------------------------------
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// Anti-Grain Geometry - Version 2.4
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// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
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//
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// Permission to copy, use, modify, sell and distribute this software
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// is granted provided this copyright notice appears in all copies.
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// This software is provided "as is" without express or implied
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// warranty, and with no claim as to its suitability for any purpose.
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//
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//----------------------------------------------------------------------------
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// Contact: mcseem@antigrain.com
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// mcseemagg@yahoo.com
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// http://www.antigrain.com
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//----------------------------------------------------------------------------
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//
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// Affine transformation classes.
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//
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//----------------------------------------------------------------------------
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#ifndef AGG_TRANS_AFFINE_INCLUDED
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#define AGG_TRANS_AFFINE_INCLUDED
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#include <math.h>
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#include "agg_basics.h"
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namespace agg
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{
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const double affine_epsilon = 1e-14;
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//============================================================trans_affine
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//
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// See Implementation agg_trans_affine.cpp
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//
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// Affine transformation are linear transformations in Cartesian coordinates
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// (strictly speaking not only in Cartesian, but for the beginning we will
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// think so). They are rotation, scaling, translation and skewing.
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// After any affine transformation a line segment remains a line segment
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// and it will never become a curve.
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//
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// There will be no math about matrix calculations, since it has been
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// described many times. Ask yourself a very simple question:
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// "why do we need to understand and use some matrix stuff instead of just
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// rotating, scaling and so on". The answers are:
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//
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// 1. Any combination of transformations can be done by only 4 multiplications
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// and 4 additions in floating point.
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// 2. One matrix transformation is equivalent to the number of consecutive
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// discrete transformations, i.e. the matrix "accumulates" all transformations
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// in the order of their settings. Suppose we have 4 transformations:
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// * rotate by 30 degrees,
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// * scale X to 2.0,
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// * scale Y to 1.5,
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// * move to (100, 100).
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// The result will depend on the order of these transformations,
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// and the advantage of matrix is that the sequence of discret calls:
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// rotate(30), scaleX(2.0), scaleY(1.5), move(100,100)
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// will have exactly the same result as the following matrix transformations:
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//
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// affine_matrix m;
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// m *= rotate_matrix(30);
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// m *= scaleX_matrix(2.0);
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// m *= scaleY_matrix(1.5);
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// m *= move_matrix(100,100);
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//
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// m.transform_my_point_at_last(x, y);
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//
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// What is the good of it? In real life we will set-up the matrix only once
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// and then transform many points, let alone the convenience to set any
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// combination of transformations.
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//
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// So, how to use it? Very easy - literally as it's shown above. Not quite,
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// let us write a correct example:
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//
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// agg::trans_affine m;
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// m *= agg::trans_affine_rotation(30.0 * 3.1415926 / 180.0);
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// m *= agg::trans_affine_scaling(2.0, 1.5);
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// m *= agg::trans_affine_translation(100.0, 100.0);
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// m.transform(&x, &y);
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//
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// The affine matrix is all you need to perform any linear transformation,
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// but all transformations have origin point (0,0). It means that we need to
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// use 2 translations if we want to rotate someting around (100,100):
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//
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// m *= agg::trans_affine_translation(-100.0, -100.0); // move to (0,0)
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// m *= agg::trans_affine_rotation(30.0 * 3.1415926 / 180.0); // rotate
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// m *= agg::trans_affine_translation(100.0, 100.0); // move back to (100,100)
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//----------------------------------------------------------------------
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struct trans_affine
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{
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double sx, shy, shx, sy, tx, ty;
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//------------------------------------------ Construction
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// Identity matrix
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trans_affine() :
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sx(1.0), shy(0.0), shx(0.0), sy(1.0), tx(0.0), ty(0.0)
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{}
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// Custom matrix. Usually used in derived classes
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trans_affine(double v0, double v1, double v2,
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double v3, double v4, double v5) :
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sx(v0), shy(v1), shx(v2), sy(v3), tx(v4), ty(v5)
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{}
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// Custom matrix from m[6]
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explicit trans_affine(const double* m) :
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sx(m[0]), shy(m[1]), shx(m[2]), sy(m[3]), tx(m[4]), ty(m[5])
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{}
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// Rectangle to a parallelogram.
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trans_affine(double x1, double y1, double x2, double y2,
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const double* parl)
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{
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rect_to_parl(x1, y1, x2, y2, parl);
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}
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// Parallelogram to a rectangle.
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trans_affine(const double* parl,
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double x1, double y1, double x2, double y2)
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{
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parl_to_rect(parl, x1, y1, x2, y2);
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}
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// Arbitrary parallelogram transformation.
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trans_affine(const double* src, const double* dst)
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{
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parl_to_parl(src, dst);
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}
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//---------------------------------- Parellelogram transformations
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// transform a parallelogram to another one. Src and dst are
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// pointers to arrays of three points (double[6], x1,y1,...) that
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// identify three corners of the parallelograms assuming implicit
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// fourth point. The arguments are arrays of double[6] mapped
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// to x1,y1, x2,y2, x3,y3 where the coordinates are:
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// *-----------------*
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// / (x3,y3)/
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// / /
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// /(x1,y1) (x2,y2)/
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// *-----------------*
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const trans_affine& parl_to_parl(const double* src,
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const double* dst);
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const trans_affine& rect_to_parl(double x1, double y1,
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double x2, double y2,
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const double* parl);
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const trans_affine& parl_to_rect(const double* parl,
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double x1, double y1,
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double x2, double y2);
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//------------------------------------------ Operations
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// Reset - load an identity matrix
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const trans_affine& reset();
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// Direct transformations operations
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const trans_affine& translate(double x, double y);
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const trans_affine& rotate(double a);
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const trans_affine& scale(double s);
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const trans_affine& scale(double x, double y);
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// Multiply matrix to another one
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const trans_affine& multiply(const trans_affine& m);
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// Multiply "m" to "this" and assign the result to "this"
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const trans_affine& premultiply(const trans_affine& m);
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// Multiply matrix to inverse of another one
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const trans_affine& multiply_inv(const trans_affine& m);
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// Multiply inverse of "m" to "this" and assign the result to "this"
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const trans_affine& premultiply_inv(const trans_affine& m);
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// Invert matrix. Do not try to invert degenerate matrices,
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// there's no check for validity. If you set scale to 0 and
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// then try to invert matrix, expect unpredictable result.
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const trans_affine& invert();
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// Mirroring around X
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const trans_affine& flip_x();
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// Mirroring around Y
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const trans_affine& flip_y();
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//------------------------------------------- Load/Store
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// Store matrix to an array [6] of double
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void store_to(double* m) const
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{
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*m++ = sx; *m++ = shy; *m++ = shx; *m++ = sy; *m++ = tx; *m++ = ty;
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}
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// Load matrix from an array [6] of double
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const trans_affine& load_from(const double* m)
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{
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sx = *m++; shy = *m++; shx = *m++; sy = *m++; tx = *m++; ty = *m++;
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return *this;
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}
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//------------------------------------------- Operators
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// Multiply the matrix by another one
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const trans_affine& operator *= (const trans_affine& m)
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{
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return multiply(m);
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}
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// Multiply the matrix by inverse of another one
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const trans_affine& operator /= (const trans_affine& m)
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{
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return multiply_inv(m);
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}
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// Multiply the matrix by another one and return
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// the result in a separete matrix.
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trans_affine operator * (const trans_affine& m) const
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{
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return trans_affine(*this).multiply(m);
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}
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// Multiply the matrix by inverse of another one
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// and return the result in a separete matrix.
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trans_affine operator / (const trans_affine& m) const
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{
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return trans_affine(*this).multiply_inv(m);
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}
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// Calculate and return the inverse matrix
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trans_affine operator ~ () const
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{
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trans_affine ret = *this;
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return ret.invert();
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}
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// Equal operator with default epsilon
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bool operator == (const trans_affine& m) const
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{
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return is_equal(m, affine_epsilon);
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}
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// Not Equal operator with default epsilon
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bool operator != (const trans_affine& m) const
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{
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return !is_equal(m, affine_epsilon);
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}
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//-------------------------------------------- Transformations
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// Direct transformation of x and y
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void transform(double* x, double* y) const;
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// Direct transformation of x and y, 2x2 matrix only, no translation
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void transform_2x2(double* x, double* y) const;
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// Inverse transformation of x and y. It works slower than the
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// direct transformation. For massive operations it's better to
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// invert() the matrix and then use direct transformations.
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void inverse_transform(double* x, double* y) const;
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//-------------------------------------------- Auxiliary
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// Calculate the determinant of matrix
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double determinant() const
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{
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return sx * sy - shy * shx;
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}
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// Calculate the reciprocal of the determinant
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double determinant_reciprocal() const
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{
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return 1.0 / (sx * sy - shy * shx);
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}
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// Get the average scale (by X and Y).
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// Basically used to calculate the approximation_scale when
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// decomposinting curves into line segments.
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double scale() const;
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// Check to see if the matrix is not degenerate
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bool is_valid(double epsilon = affine_epsilon) const;
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// Check to see if it's an identity matrix
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bool is_identity(double epsilon = affine_epsilon) const;
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// Check to see if two matrices are equal
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bool is_equal(const trans_affine& m, double epsilon = affine_epsilon) const;
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// Determine the major parameters. Use with caution considering
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// possible degenerate cases.
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double rotation() const;
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void translation(double* dx, double* dy) const;
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void scaling(double* x, double* y) const;
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void scaling_abs(double* x, double* y) const;
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};
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//------------------------------------------------------------------------
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inline void trans_affine::transform(double* x, double* y) const
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{
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double tmp = *x;
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*x = tmp * sx + *y * shx + tx;
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*y = tmp * shy + *y * sy + ty;
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}
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//------------------------------------------------------------------------
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inline void trans_affine::transform_2x2(double* x, double* y) const
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{
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double tmp = *x;
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*x = tmp * sx + *y * shx;
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*y = tmp * shy + *y * sy;
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}
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//------------------------------------------------------------------------
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inline void trans_affine::inverse_transform(double* x, double* y) const
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{
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double d = determinant_reciprocal();
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double a = (*x - tx) * d;
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double b = (*y - ty) * d;
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*x = a * sy - b * shx;
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*y = b * sx - a * shy;
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}
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//------------------------------------------------------------------------
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inline double trans_affine::scale() const
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{
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double x = 0.707106781 * sx + 0.707106781 * shx;
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double y = 0.707106781 * shy + 0.707106781 * sy;
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return sqrt(x*x + y*y);
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::translate(double x, double y)
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{
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tx += x;
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ty += y;
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return *this;
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::rotate(double a)
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{
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double ca = cos(a);
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double sa = sin(a);
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double t0 = sx * ca - shy * sa;
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double t2 = shx * ca - sy * sa;
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double t4 = tx * ca - ty * sa;
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shy = sx * sa + shy * ca;
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sy = shx * sa + sy * ca;
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ty = tx * sa + ty * ca;
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sx = t0;
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shx = t2;
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tx = t4;
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return *this;
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::scale(double x, double y)
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{
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double mm0 = x; // Possible hint for the optimizer
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double mm3 = y;
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sx *= mm0;
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shx *= mm0;
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tx *= mm0;
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shy *= mm3;
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sy *= mm3;
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ty *= mm3;
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return *this;
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::scale(double s)
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{
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double m = s; // Possible hint for the optimizer
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sx *= m;
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shx *= m;
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tx *= m;
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shy *= m;
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sy *= m;
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ty *= m;
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return *this;
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::premultiply(const trans_affine& m)
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{
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trans_affine t = m;
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return *this = t.multiply(*this);
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::multiply_inv(const trans_affine& m)
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{
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trans_affine t = m;
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t.invert();
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return multiply(t);
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}
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//------------------------------------------------------------------------
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inline const trans_affine& trans_affine::premultiply_inv(const trans_affine& m)
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{
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trans_affine t = m;
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t.invert();
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return *this = t.multiply(*this);
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}
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//------------------------------------------------------------------------
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inline void trans_affine::scaling_abs(double* x, double* y) const
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{
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// Used to calculate scaling coefficients in image resampling.
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// When there is considerable shear this method gives us much
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// better estimation than just sx, sy.
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*x = sqrt(sx * sx + shx * shx);
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*y = sqrt(shy * shy + sy * sy);
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}
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//====================================================trans_affine_rotation
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// Rotation matrix. sin() and cos() are calculated twice for the same angle.
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// There's no harm because the performance of sin()/cos() is very good on all
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// modern processors. Besides, this operation is not going to be invoked too
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// often.
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class trans_affine_rotation : public trans_affine
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{
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public:
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trans_affine_rotation(double a) :
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trans_affine(cos(a), sin(a), -sin(a), cos(a), 0.0, 0.0)
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{}
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};
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//====================================================trans_affine_scaling
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// Scaling matrix. x, y - scale coefficients by X and Y respectively
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class trans_affine_scaling : public trans_affine
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{
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public:
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trans_affine_scaling(double x, double y) :
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trans_affine(x, 0.0, 0.0, y, 0.0, 0.0)
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{}
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trans_affine_scaling(double s) :
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trans_affine(s, 0.0, 0.0, s, 0.0, 0.0)
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{}
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};
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//================================================trans_affine_translation
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// Translation matrix
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class trans_affine_translation : public trans_affine
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{
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public:
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trans_affine_translation(double x, double y) :
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trans_affine(1.0, 0.0, 0.0, 1.0, x, y)
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{}
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};
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//====================================================trans_affine_skewing
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// Sckewing (shear) matrix
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class trans_affine_skewing : public trans_affine
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{
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public:
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trans_affine_skewing(double x, double y) :
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trans_affine(1.0, tan(y), tan(x), 1.0, 0.0, 0.0)
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{}
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};
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//===============================================trans_affine_line_segment
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// Rotate, Scale and Translate, associating 0...dist with line segment
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// x1,y1,x2,y2
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class trans_affine_line_segment : public trans_affine
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{
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public:
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trans_affine_line_segment(double x1, double y1, double x2, double y2,
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double dist)
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{
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double dx = x2 - x1;
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double dy = y2 - y1;
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if(dist > 0.0)
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{
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multiply(trans_affine_scaling(sqrt(dx * dx + dy * dy) / dist));
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}
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multiply(trans_affine_rotation(atan2(dy, dx)));
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multiply(trans_affine_translation(x1, y1));
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}
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};
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//============================================trans_affine_reflection_unit
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// Reflection matrix. Reflect coordinates across the line through
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// the origin containing the unit vector (ux, uy).
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// Contributed by John Horigan
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class trans_affine_reflection_unit : public trans_affine
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{
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public:
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trans_affine_reflection_unit(double ux, double uy) :
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trans_affine(2.0 * ux * ux - 1.0,
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2.0 * ux * uy,
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2.0 * ux * uy,
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2.0 * uy * uy - 1.0,
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0.0, 0.0)
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{}
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};
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//=================================================trans_affine_reflection
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// Reflection matrix. Reflect coordinates across the line through
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// the origin at the angle a or containing the non-unit vector (x, y).
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// Contributed by John Horigan
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class trans_affine_reflection : public trans_affine_reflection_unit
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{
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public:
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trans_affine_reflection(double a) :
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trans_affine_reflection_unit(cos(a), sin(a))
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{}
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trans_affine_reflection(double x, double y) :
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trans_affine_reflection_unit(x / sqrt(x * x + y * y), y / sqrt(x * x + y * y))
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{}
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};
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}
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#endif
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