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286 lines
8.0 KiB
C++
286 lines
8.0 KiB
C++
/* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#ifndef GFX_MATRIX_H
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#define GFX_MATRIX_H
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#include "gfxPoint.h"
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#include "gfxTypes.h"
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#include "gfxRect.h"
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// XX - I don't think this class should use gfxFloat at all,
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// but should use 'double' and be called gfxDoubleMatrix;
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// we can then typedef that to gfxMatrix where we typedef
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// double to be gfxFloat.
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/**
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* A matrix that represents an affine transformation. Projective
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* transformations are not supported. This matrix looks like:
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*
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* / a b 0 \
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* | c d 0 |
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* \ tx ty 1 /
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*
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* So, transforming a point (x, y) results in:
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*
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* / a b 0 \ / a * x + c * y + tx \ T
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* (x y 1) * | c d 0 | = | b * x + d * y + ty |
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* \ tx ty 1 / \ 1 /
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*
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*/
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struct gfxMatrix {
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double xx; double yx;
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double xy; double yy;
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double x0; double y0;
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public:
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/**
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* Initializes this matrix as the identity matrix.
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*/
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gfxMatrix() { Reset(); }
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/**
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* Initializes the matrix from individual components. See the class
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* description for the layout of the matrix.
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*/
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gfxMatrix(gfxFloat a, gfxFloat b, gfxFloat c, gfxFloat d, gfxFloat tx, gfxFloat ty) :
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xx(a), yx(b),
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xy(c), yy(d),
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x0(tx), y0(ty) { }
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/**
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* Post-multiplies m onto the matrix.
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*/
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const gfxMatrix& operator *= (const gfxMatrix& m) {
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return Multiply(m);
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}
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/**
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* Multiplies *this with m and returns the result.
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*/
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gfxMatrix operator * (const gfxMatrix& m) const {
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return gfxMatrix(*this).Multiply(m);
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}
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/* Returns true if the other matrix is fuzzy-equal to this matrix.
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* Note that this isn't a cheap comparison!
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*/
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bool operator==(const gfxMatrix& other) const
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{
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return FuzzyEqual(xx, other.xx) && FuzzyEqual(yx, other.yx) &&
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FuzzyEqual(xy, other.xy) && FuzzyEqual(yy, other.yy) &&
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FuzzyEqual(x0, other.x0) && FuzzyEqual(y0, other.y0);
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}
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bool operator!=(const gfxMatrix& other) const
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{
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return !(*this == other);
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}
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// matrix operations
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/**
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* Resets this matrix to the identity matrix.
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*/
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const gfxMatrix& Reset();
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bool IsIdentity() const {
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return xx == 1.0 && yx == 0.0 &&
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xy == 0.0 && yy == 1.0 &&
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x0 == 0.0 && y0 == 0.0;
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}
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/**
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* Inverts this matrix, if possible. Otherwise, the matrix is left
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* unchanged.
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*
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* XXX should this do something with the return value of
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* cairo_matrix_invert?
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*/
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const gfxMatrix& Invert();
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/**
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* Check if matrix is singular (no inverse exists).
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*/
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bool IsSingular() const {
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// if the determinant (ad - bc) is zero it's singular
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return (xx * yy) == (yx * xy);
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}
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/**
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* Scales this matrix. The scale is pre-multiplied onto this matrix,
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* i.e. the scaling takes place before the other transformations.
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*/
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const gfxMatrix& Scale(gfxFloat x, gfxFloat y);
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/**
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* Translates this matrix. The translation is pre-multiplied onto this matrix,
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* i.e. the translation takes place before the other transformations.
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*/
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const gfxMatrix& Translate(const gfxPoint& pt);
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/**
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* Rotates this matrix. The rotation is pre-multiplied onto this matrix,
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* i.e. the translation takes place after the other transformations.
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*
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* @param radians Angle in radians.
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*/
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const gfxMatrix& Rotate(gfxFloat radians);
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/**
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* Multiplies the current matrix with m.
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* This is a post-multiplication, i.e. the transformations of m are
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* applied _after_ the existing transformations.
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*
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* XXX is that difference (compared to Rotate etc) a good thing?
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*/
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const gfxMatrix& Multiply(const gfxMatrix& m);
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/**
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* Multiplies the current matrix with m.
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* This is a pre-multiplication, i.e. the transformations of m are
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* applied _before_ the existing transformations.
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*/
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const gfxMatrix& PreMultiply(const gfxMatrix& m);
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/**
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* Transforms a point according to this matrix.
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*/
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gfxPoint Transform(const gfxPoint& point) const;
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/**
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* Transform a distance according to this matrix. This does not apply
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* any translation components.
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*/
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gfxSize Transform(const gfxSize& size) const;
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/**
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* Transforms both the point and distance according to this matrix.
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*/
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gfxRect Transform(const gfxRect& rect) const;
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gfxRect TransformBounds(const gfxRect& rect) const;
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/**
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* Returns the translation component of this matrix.
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*/
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gfxPoint GetTranslation() const {
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return gfxPoint(x0, y0);
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}
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/**
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* Returns true if the matrix is anything other than a straight
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* translation by integers.
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*/
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bool HasNonIntegerTranslation() const {
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return HasNonTranslation() ||
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!FuzzyEqual(x0, floor(x0 + 0.5)) ||
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!FuzzyEqual(y0, floor(y0 + 0.5));
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}
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/**
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* Returns true if the matrix has any transform other
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* than a straight translation
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*/
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bool HasNonTranslation() const {
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return !FuzzyEqual(xx, 1.0) || !FuzzyEqual(yy, 1.0) ||
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!FuzzyEqual(xy, 0.0) || !FuzzyEqual(yx, 0.0);
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}
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/**
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* Returns true if the matrix only has an integer translation.
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*/
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bool HasOnlyIntegerTranslation() const {
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return !HasNonIntegerTranslation();
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}
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/**
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* Returns true if the matrix has any transform other
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* than a translation or a -1 y scale (y axis flip)
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*/
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bool HasNonTranslationOrFlip() const {
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return !FuzzyEqual(xx, 1.0) ||
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(!FuzzyEqual(yy, 1.0) && !FuzzyEqual(yy, -1.0)) ||
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!FuzzyEqual(xy, 0.0) || !FuzzyEqual(yx, 0.0);
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}
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/**
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* Returns true if the matrix has any transform other
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* than a translation or scale; this is, if there is
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* no rotation.
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*/
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bool HasNonAxisAlignedTransform() const {
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return !FuzzyEqual(xy, 0.0) || !FuzzyEqual(yx, 0.0);
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}
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/**
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* Computes the determinant of this matrix.
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*/
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double Determinant() const {
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return xx*yy - yx*xy;
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}
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/* Computes the scale factors of this matrix; that is,
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* the amounts each basis vector is scaled by.
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* The xMajor parameter indicates if the larger scale is
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* to be assumed to be in the X direction or not.
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*/
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gfxSize ScaleFactors(bool xMajor) const {
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double det = Determinant();
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if (det == 0.0)
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return gfxSize(0.0, 0.0);
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gfxSize sz = xMajor ? gfxSize(1.0, 0.0) : gfxSize(0.0, 1.0);
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sz = Transform(sz);
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double major = sqrt(sz.width * sz.width + sz.height * sz.height);
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double minor = 0.0;
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// ignore mirroring
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if (det < 0.0)
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det = - det;
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if (major)
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minor = det / major;
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if (xMajor)
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return gfxSize(major, minor);
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return gfxSize(minor, major);
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}
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/**
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* Snap matrix components that are close to integers
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* to integers. In particular, components that are integral when
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* converted to single precision are set to those integers.
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*/
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void NudgeToIntegers(void);
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/**
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* Returns true if matrix is multiple of 90 degrees rotation with flipping,
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* scaling and translation.
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*/
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bool PreservesAxisAlignedRectangles() const {
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return ((FuzzyEqual(xx, 0.0) && FuzzyEqual(yy, 0.0))
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|| (FuzzyEqual(xy, 0.0) && FuzzyEqual(yx, 0.0)));
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}
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/**
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* Returns true if the matrix has non-integer scale
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*/
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bool HasNonIntegerScale() const {
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return !FuzzyEqual(xx, floor(xx + 0.5)) ||
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!FuzzyEqual(yy, floor(yy + 0.5));
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}
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private:
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static bool FuzzyEqual(gfxFloat aV1, gfxFloat aV2) {
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return fabs(aV2 - aV1) < 1e-6;
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}
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};
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#endif /* GFX_MATRIX_H */
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