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/*****
* transform.h
* Andy Hammerlindl 2002/05/22
*
* The transform datatype stores an affine transformation on the plane
* The datamembers are x, y, xx, xy, yx, and yy. A pair (x,y) is
* transformed as
* x' = t.x + t.xx * x + t.xy * y
* y' = t.y + t.yx * x + t.yy * y
*****/
#ifndef TRANSFORM_H
#define TRANSFORM_H
#include <iostream>
#include "pair.h"
namespace camp {
class transform : public gc {
double x;
double y;
double xx;
double xy;
double yx;
double yy;
public:
transform()
: x(0.0), y(0.0), xx(1.0), xy(0.0), yx(0.0), yy(1.0) {}
virtual ~transform() {}
transform(double x, double y,
double xx, double xy,
double yx, double yy)
: x(x), y(y), xx(xx), xy(xy), yx(yx), yy(yy) {}
double getx() const { return x; }
double gety() const { return y; }
double getxx() const { return xx; }
double getxy() const { return xy; }
double getyx() const { return yx; }
double getyy() const { return yy; }
friend transform operator+ (const transform& t, const transform& s)
{
return transform(t.x + s.x, t.y + s.y,
t.xx + s.xx, t.xy + s.xy,
t.yx + s.yx, t.yy + s.yy);
}
friend transform operator- (const transform& t, const transform& s)
{
return transform(t.x - s.x, t.y - s.y,
t.xx - s.xx, t.xy - s.xy,
t.yx - s.yx, t.yy - s.yy);
}
friend transform operator- (const transform& t)
{
return transform(-t.x, -t.y,
-t.xx, -t.xy,
-t.yx, -t.yy);
}
friend pair operator* (const transform& t, const pair& z)
{
double x = z.getx(), y = z.gety();
return pair(t.x + t.xx * x + t.xy * y, t.y + t.yx * x + t.yy * y);
}
// Calculates the composition of t and s, so for a pair, z,
// t * (s * z) == (t * s) * z
// Can be thought of as matrix multiplication.
friend transform operator* (const transform& t, const transform& s)
{
return transform(t.x + t.xx * s.x + t.xy * s.y,
t.y + t.yx * s.x + t.yy * s.y,
t.xx * s.xx + t.xy * s.yx,
t.xx * s.xy + t.xy * s.yy,
t.yx * s.xx + t.yy * s.yx,
t.yx * s.xy + t.yy * s.yy);
}
friend bool operator== (const transform& t1, const transform& t2)
{
return t1.x == t2.x && t1.y == t2.y &&
t1.xx == t2.xx && t1.xy == t2.xy &&
t1.yx == t2.yx && t1.yy == t2.yy;
}
friend bool operator!= (const transform& t1, const transform& t2)
{
return !(t1 == t2);
}
bool isIdentity() const
{
return x == 0.0 && y == 0.0 &&
xx == 1.0 && xy == 0.0 && yx == 0.0 && yy == 1.0;
}
bool isNull() const
{
return x == 0.0 && y == 0.0 &&
xx == 0.0 && xy == 0.0 && yx == 0.0 && yy == 0.0;
}
// Calculates the determinant, as if it were a matrix.
friend double det(const transform& t)
{
return t.xx * t.yy - t.xy * t.yx;
}
// Tells if the transformation is invertible (bijective).
bool invertible() const
{
return det(*this) != 0.0;
}
friend transform inverse(const transform& t)
{
double d = det(t);
if (d == 0.0)
reportError("inverting singular transform");
d=1.0/d;
return transform((t.xy * t.y - t.yy * t.x)*d,
(t.yx * t.x - t.xx * t.y)*d,
t.yy*d, -t.xy*d, -t.yx*d, t.xx*d);
}
friend ostream& operator<< (ostream& out, const transform& t)
{
return out << "(" << t.x << ","
<< t.y << ","
<< t.xx << ","
<< t.xy << ","
<< t.yx << ","
<< t.yy << ")";
}
};
// The common transforms
static const transform identity;
inline transform shift(pair z)
{
return transform (z.getx(), z.gety(), 1.0, 0.0, 0.0, 1.0);
}
inline transform xscale(double s)
{
return transform (0.0, 0.0, s, 0.0, 0.0, 1.0);
}
inline transform yscale(double s)
{
return transform (0.0, 0.0, 1.0, 0.0, 0.0, s);
}
inline transform scale(double s)
{
return transform (0.0, 0.0, s, 0.0, 0.0, s);
}
inline transform scale(pair z)
{
// Equivalent to multiplication by z.
double x = z.getx(), y = z.gety();
return transform (0.0, 0.0, x, -y, y, x);
}
inline transform slant(double s)
{
return transform (0.0, 0.0, 1.0, s, 0.0, 1.0);
}
inline transform rotate(double theta)
{
double s = sin(theta), c = cos(theta);
return transform (0.0, 0.0, c, -s, s, c);
}
// return rotate(angle(v)) if z != (0,0); otherwise return identity.
inline transform rotate(pair z)
{
double d=z.length();
if(d == 0.0) return identity;
d=1.0/d;
return transform (0.0, 0.0, d*z.getx(), -d*z.gety(), d*z.gety(), d*z.getx());
}
inline transform rotatearound(pair z, double theta)
{
// Notice the operators are applied from right to left.
// Could be optimized.
return shift(z) * rotate(theta) * shift(-z);
}
inline transform reflectabout(pair z, pair w)
{
if (z == w)
reportError("points determining line to reflect about must be distinct");
// Also could be optimized.
transform basis = shift(z) * scale(w-z);
transform flip = yscale(-1.0);
return basis * flip * inverse(basis);
}
// Remove the x and y components, so the new transform maps zero to zero.
inline transform shiftless(transform t)
{
return transform(0, 0, t.getxx(), t.getxy(), t.getyx(), t.getyy());
}
// Return the translational component of t.
inline transform shift(transform t)
{
return transform(t.getx(), t.gety(), 1.0, 0, 0, 1.0);
}
// Return the translational component of t.
inline pair shiftpair(transform t)
{
return (t.getx(), t.gety());
}
inline transform matrix(pair lb, pair rt)
{
pair size=rt-lb;
return transform(lb.getx(),lb.gety(),size.getx(),0,0,size.gety());
}
} //namespace camp
GC_DECLARE_PTRFREE(camp::transform);
#endif
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