package edu.berkeley.qfat.geom;
+import javax.media.opengl.*;
-/** affine matrix; immutable */
+// FEATURE: precompute/cache determinant?
+
+/** an affine matrix; immutable */
public class Matrix {
- //
- // [ a b c d ] [ x ]
- // [ e f g h ] [ y ]
- // [ i j k l ] [ z ]
- // [ m n o p ] [ 1 ]
- //
+
+ /**
+ * <pre>
+ * [ a b c d ] [ x ]
+ * [ e f g h ] [ y ]
+ * [ i j k l ] [ z ]
+ * [ m n o p ] [ 1 ]
+ * </pre>
+ */
public final float a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p;
- public Matrix() { this(1); }
- public Matrix(float scale) {
- a = f = k = scale;
- l = h = d = e = b = i = c = j = g = 0;
- m = n = o = 0;
- p = 1;
- }
- public Matrix(float scalex, float scaley, float scalez) {
- a = scalex;
- f = scaley;
- k = scalez;
- l = h = d = e = b = i = c = j = g = 0;
- m = n = o = 0;
- p = 1;
- }
- public Matrix(Vec translate) {
- d = translate.x; h = translate.y; l = translate.z;
- a = f = k = 1;
- b = c = e = g = i = j = 0;
- m = n = o = 0;
- p = 1;
+
+ /** the zero matrix */
+ public static final Matrix ZERO = new Matrix(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0);
+
+ /** the identity matrix */
+ public static final Matrix ONE = new Matrix(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1);
+
+ /** the identity matrix */
+ public static final Matrix NEGATIVE_ONE = new Matrix(-1,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,1);
+
+ public Matrix(double a, double b, double c, double d, double e, double f, double g,
+ double h, double i, double j, double k, double l, double m, double n, double o, double p) {
+ this((float)a, (float)b, (float)c, (float)d,
+ (float)e, (float)f, (float)g, (float)h,
+ (float)i, (float)j, (float)k, (float)l,
+ (float)m, (float)n, (float)o, (float)p);
}
+
public Matrix(float a, float b, float c, float d, float e, float f, float g,
float h, float i, float j, float k, float l, float m, float n, float o, float p) {
this.a = a; this.b = b; this.c = c; this.d = d; this.e = e; this.f = f; this.g = g; this.h = h; this.i = i;
this.j = j; this.k = k; this.l = l; this.m = m; this.n = n; this.o = o; this.p = p;
}
+
+ /** a scaling matrix (uniform in all dimensions) */
+ public static Matrix scale(float scale) { return scale(scale, scale, scale); }
+
+ /** a scaling matrix */
+ public static Matrix scale(float scalex, float scaley, float scalez) {
+ return new Matrix(scalex, 0, 0, 0, 0, scaley, 0, 0, 0, 0, scalez, 0, 0, 0, 0, 1); }
+
+ /** a translation matrix */
+ public static Matrix translate(Vec translate) {
+ return new Matrix(1, 0, 0, translate.x,
+ 0, 1, 0, translate.y,
+ 0, 0, 1, translate.z,
+ 0, 0, 0, 1);
+ }
+
+ /** a rotation matrix, <tt>angle</tt> degrees around <tt>axis</tt> */
+ public static Matrix rotate(Vec axis, float angle) {
+ float q = (float)Math.cos(angle);
+ float s = (float)Math.sin(angle);
+ float t = 1 - q;
+ float a = (float)(q + axis.x*axis.x*t);
+ float f = (float)(q + axis.y*axis.y*t);
+ float k = (float)(q + axis.z*axis.z*t);
+ float tmp1 = axis.x*axis.y*t;
+ float tmp2 = axis.z*s;
+ float e = (float)(tmp1 + tmp2);
+ float b = (float)(tmp1 - tmp2);
+ tmp1 = axis.x*axis.z*t;
+ tmp2 = axis.y*s;
+ float i = (float)(tmp1 - tmp2);
+ float c = (float)(tmp1 + tmp2);
+ tmp1 = axis.y*axis.z*t;
+ tmp2 = axis.x*s;
+ float j = (float)(tmp1 + tmp2);
+ float g = (float)(tmp1 - tmp2);
+ return new Matrix(a, b, c, 0,
+ e, f, g, 0,
+ i, j, k, 0,
+ 0, 0, 0, 1);
+ }
+
+ public static Matrix reflect(Vec v) {
+ Vec reflectionPlaneNormal = v.norm();
+ float a = reflectionPlaneNormal.x;
+ float b = reflectionPlaneNormal.y;
+ float c = reflectionPlaneNormal.z;
+ return
+ new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
+ -2*a*b, 1-2*b*b, -2*b*c, 0,
+ -2*a*c, -2*b*c, 1-2*c*c, 0,
+ 0, 0, 0, 1);
+ }
+
+ public Vec getTranslationalComponent() {
+ return new Vec(d, h, l);
+ }
+
public Matrix plus(Matrix x) {
return new Matrix(a+x.a, b+x.b, c+x.c, d+x.d, e+x.e, f+x.f, g+x.g, h+x.h, i+x.i, j+x.j, k+x.k, l+x.l, m+x.m, n+x.n, o+x.o, p+x.p);
}
+ public Matrix minus(Matrix x) {
+ return new Matrix(a-x.a, b-x.b, c-x.c, d-x.d, e-x.e, f-x.f, g-x.g, h-x.h, i-x.i, j-x.j, k-x.k, l-x.l, m-x.m, n-x.n, o-x.o, p-x.p);
+ }
public Matrix times(float x) {
return new Matrix(a*x, b*x, c*x, d*x, e*x, f*x, g*x, h*x, i*x, j*x, k*x, l*x, m*x, n*x, o*x, p*x);
}
return ret;
}
- public Matrix(Vec axis, float angle) {
- double q = Math.cos(angle);
- double s = Math.sin(angle);
- double t = 1.0 - q;
- a = (float)(q + axis.x*axis.x*t);
- f = (float)(q + axis.y*axis.y*t);
- k = (float)(q + axis.z*axis.z*t);
- double tmp1 = axis.x*axis.y*t;
- double tmp2 = axis.z*s;
- e = (float)(tmp1 + tmp2);
- b = (float)(tmp1 - tmp2);
- tmp1 = axis.x*axis.z*t;
- tmp2 = axis.y*s;
- i = (float)(tmp1 - tmp2);
- c = (float)(tmp1 + tmp2);
- tmp1 = axis.y*axis.z*t;
- tmp2 = axis.x*s;
- j = (float)(tmp1 + tmp2);
- g = (float)(tmp1 - tmp2);
- d = h = l = 0;
- m = n = o = 0;
- p = 1;
- }
+ /** discards bottom row */
public Point times(Point p) {
// discards bottom row
- return new Point(a*p.x + b*p.y + c*p.z + d,
- e*p.x + f*p.y + g*p.z + h,
- i*p.x + j*p.y + k*p.z + l);
+ double x = a*p.x + b*p.y + c*p.z + d;
+ double y = e*p.x + f*p.y + g*p.z + h;
+ double z = i*p.x + j*p.y + k*p.z + l;
+ double q = m*p.x + n*p.y + o*p.z + this.p;
+ return new Point(x/q, y/q, z/q);
}
+
+ /** discards bottom row */
public Vec times(Vec p) {
- // discards bottom row
return new Vec(a*p.x + b*p.y + c*p.z + d,
e*p.x + f*p.y + g*p.z + h,
i*p.x + j*p.y + k*p.z + l);
}
- public Point apply(Point p) { return p; }
- public Vec apply(Vec v) { return v; }
- public Matrix invert() { return this; }
- public Matrix times(Matrix m) { return this; }
+
+ public Matrix preMultiplyTranslationalComponentBy(Matrix mm) {
+ Vec v = mm.times(getTranslationalComponent());
+ return new Matrix(a, b, c, v.x,
+ e, f, g, v.y,
+ i, j, k, v.z,
+ m, n, o, 1);
+ }
+
+ /** multiply by another matrix */
+ public Matrix times(Matrix z) {
+ float t00 = a;
+ float t01 = b;
+ float t02 = c;
+ float t03 = d;
+ float t10 = e;
+ float t11 = f;
+ float t12 = g;
+ float t13 = h;
+ float t20 = i;
+ float t21 = j;
+ float t22 = k;
+ float t23 = l;
+ float t30 = m;
+ float t31 = n;
+ float t32 = o;
+ float t33 = p;
+ float m00 = z.a;
+ float m01 = z.b;
+ float m02 = z.c;
+ float m03 = z.d;
+ float m10 = z.e;
+ float m11 = z.f;
+ float m12 = z.g;
+ float m13 = z.h;
+ float m20 = z.i;
+ float m21 = z.j;
+ float m22 = z.k;
+ float m23 = z.l;
+ float m30 = z.m;
+ float m31 = z.n;
+ float m32 = z.o;
+ float m33 = z.p;
+ return new Matrix(t00*m00 + t01*m10 + t02*m20 + t03*m30,
+ t00*m01 + t01*m11 + t02*m21 + t03*m31,
+ t00*m02 + t01*m12 + t02*m22 + t03*m32,
+ t00*m03 + t01*m13 + t02*m23 + t03*m33,
+ t10*m00 + t11*m10 + t12*m20 + t13*m30,
+ t10*m01 + t11*m11 + t12*m21 + t13*m31,
+ t10*m02 + t11*m12 + t12*m22 + t13*m32,
+ t10*m03 + t11*m13 + t12*m23 + t13*m33,
+ t20*m00 + t21*m10 + t22*m20 + t23*m30,
+ t20*m01 + t21*m11 + t22*m21 + t23*m31,
+ t20*m02 + t21*m12 + t22*m22 + t23*m32,
+ t20*m03 + t21*m13 + t22*m23 + t23*m33,
+ t30*m00 + t31*m10 + t32*m20 + t33*m30,
+ t30*m01 + t31*m11 + t32*m21 + t33*m31,
+ t30*m02 + t31*m12 + t32*m22 + t33*m32,
+ t30*m03 + t31*m13 + t32*m23 + t33*m33);
+ }
+
+ /** compute the determinant of the matrix */
+ public float determinant() {
+ float m00 = a;
+ float m01 = b;
+ float m02 = c;
+ float m03 = d;
+ float m10 = e;
+ float m11 = f;
+ float m12 = g;
+ float m13 = h;
+ float m20 = i;
+ float m21 = j;
+ float m22 = k;
+ float m23 = l;
+ float m30 = m;
+ float m31 = n;
+ float m32 = o;
+ float m33 = p;
+ return
+ m03 * m12 * m21 * m30-m02 * m13 * m21 * m30-m03 * m11 * m22 * m30+m01 * m13 * m22 * m30+
+ m02 * m11 * m23 * m30-m01 * m12 * m23 * m30-m03 * m12 * m20 * m31+m02 * m13 * m20 * m31+
+ m03 * m10 * m22 * m31-m00 * m13 * m22 * m31-m02 * m10 * m23 * m31+m00 * m12 * m23 * m31+
+ m03 * m11 * m20 * m32-m01 * m13 * m20 * m32-m03 * m10 * m21 * m32+m00 * m13 * m21 * m32+
+ m01 * m10 * m23 * m32-m00 * m11 * m23 * m32-m02 * m11 * m20 * m33+m01 * m12 * m20 * m33+
+ m02 * m10 * m21 * m33-m00 * m12 * m21 * m33-m01 * m10 * m22 * m33+m00 * m11 * m22 * m33;
+ }
+
+ /** compute the inverse of the matrix, returns null if not invertible */
+ public Matrix inverse() {
+ float determinant = determinant();
+ if (determinant==0) return null;
+ float m00 = a;
+ float m01 = b;
+ float m02 = c;
+ float m03 = d;
+ float m10 = e;
+ float m11 = f;
+ float m12 = g;
+ float m13 = h;
+ float m20 = i;
+ float m21 = j;
+ float m22 = k;
+ float m23 = l;
+ float m30 = m;
+ float m31 = n;
+ float m32 = o;
+ float m33 = p;
+ return
+ new Matrix(m12*m23*m31 - m13*m22*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 + m11*m22*m33,
+ m03*m22*m31 - m02*m23*m31 - m03*m21*m32 + m01*m23*m32 + m02*m21*m33 - m01*m22*m33,
+ m02*m13*m31 - m03*m12*m31 + m03*m11*m32 - m01*m13*m32 - m02*m11*m33 + m01*m12*m33,
+ m03*m12*m21 - m02*m13*m21 - m03*m11*m22 + m01*m13*m22 + m02*m11*m23 - m01*m12*m23,
+ m13*m22*m30 - m12*m23*m30 - m13*m20*m32 + m10*m23*m32 + m12*m20*m33 - m10*m22*m33,
+ m02*m23*m30 - m03*m22*m30 + m03*m20*m32 - m00*m23*m32 - m02*m20*m33 + m00*m22*m33,
+ m03*m12*m30 - m02*m13*m30 - m03*m10*m32 + m00*m13*m32 + m02*m10*m33 - m00*m12*m33,
+ m02*m13*m20 - m03*m12*m20 + m03*m10*m22 - m00*m13*m22 - m02*m10*m23 + m00*m12*m23,
+ m11*m23*m30 - m13*m21*m30 + m13*m20*m31 - m10*m23*m31 - m11*m20*m33 + m10*m21*m33,
+ m03*m21*m30 - m01*m23*m30 - m03*m20*m31 + m00*m23*m31 + m01*m20*m33 - m00*m21*m33,
+ m01*m13*m30 - m03*m11*m30 + m03*m10*m31 - m00*m13*m31 - m01*m10*m33 + m00*m11*m33,
+ m03*m11*m20 - m01*m13*m20 - m03*m10*m21 + m00*m13*m21 + m01*m10*m23 - m00*m11*m23,
+ m12*m21*m30 - m11*m22*m30 - m12*m20*m31 + m10*m22*m31 + m11*m20*m32 - m10*m21*m32,
+ m01*m22*m30 - m02*m21*m30 + m02*m20*m31 - m00*m22*m31 - m01*m20*m32 + m00*m21*m32,
+ m02*m11*m30 - m01*m12*m30 - m02*m10*m31 + m00*m12*m31 + m01*m10*m32 - m00*m11*m32,
+ m01*m12*m20 - m02*m11*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 + m00*m11*m22)
+ .times(1/determinant);
+ }
+
+ public String toString() {
+ return
+ "\n [ " + a + "\t" + b + "\t" + c + "\t" + d + "\t" + "]" +
+ "\n [ " + e + "\t" + f + "\t" + g + "\t" + h + "\t" + "]" +
+ "\n [ " + i + "\t" + j + "\t" + k + "\t" + l + "\t" + "]" +
+ "\n [ " + m + "\t" + n + "\t" + o + "\t" + p + "\t" + "]\n";
+ }
+
+ public boolean equals(Object oo) {
+ if (oo==null) return false;
+ if (!(oo instanceof Matrix)) return false;
+ Matrix z = (Matrix)oo;
+ return
+ near(a,z.a) &&
+ near(b,z.b) &&
+ near(c,z.c) &&
+ near(d,z.d) &&
+ near(e,z.e) &&
+ near(f,z.f) &&
+ near(g,z.g) &&
+ near(h,z.h) &&
+ near(i,z.i) &&
+ near(j,z.j) &&
+ near(k,z.k) &&
+ near(l,z.l) &&
+ near(m,z.m) &&
+ near(n,z.n) &&
+ near(o,z.o) &&
+ near(p,z.p);
+ }
+ private static final float EPSILON = 0.001f;
+ private static boolean near(float a, float b) { return Math.abs(a-b)<EPSILON; }
+
+ public int hashCode() {
+ return
+ Float.floatToIntBits(a) ^
+ Float.floatToIntBits(b) ^
+ Float.floatToIntBits(c) ^
+ Float.floatToIntBits(d) ^
+ Float.floatToIntBits(e) ^
+ Float.floatToIntBits(f) ^
+ Float.floatToIntBits(g) ^
+ Float.floatToIntBits(h) ^
+ Float.floatToIntBits(i) ^
+ Float.floatToIntBits(j) ^
+ Float.floatToIntBits(k) ^
+ Float.floatToIntBits(l) ^
+ Float.floatToIntBits(m) ^
+ Float.floatToIntBits(n) ^
+ Float.floatToIntBits(o) ^
+ Float.floatToIntBits(p);
+ }
+
+ public static Matrix getProjectionMatrix(GL gl) {
+ int view[] = new int[4];
+ double mvmatrix[] = new double[16];
+ double projmatrix[] = new double[16];
+ gl.glGetIntegerv(GL.GL_VIEWPORT, view, 0);
+ gl.glGetDoublev(GL.GL_MODELVIEW_MATRIX, mvmatrix, 0);
+ gl.glGetDoublev(GL.GL_PROJECTION_MATRIX, projmatrix, 0);
+ Matrix m = new Matrix(mvmatrix[0],
+ mvmatrix[4],
+ mvmatrix[8],
+ mvmatrix[12],
+ mvmatrix[1],
+ mvmatrix[5],
+ mvmatrix[9],
+ mvmatrix[13],
+ mvmatrix[2],
+ mvmatrix[6],
+ mvmatrix[10],
+ mvmatrix[14],
+ mvmatrix[3],
+ mvmatrix[7],
+ mvmatrix[11],
+ mvmatrix[15]);
+ Matrix p = new Matrix(projmatrix[0],
+ projmatrix[4],
+ projmatrix[8],
+ projmatrix[12],
+ projmatrix[1],
+ projmatrix[5],
+ projmatrix[9],
+ projmatrix[13],
+ projmatrix[2],
+ projmatrix[6],
+ projmatrix[10],
+ projmatrix[14],
+ projmatrix[3],
+ projmatrix[7],
+ projmatrix[11],
+ projmatrix[15]);
+ Matrix z =
+ new Matrix(0.5*view[2], 0, 0, view[0]+view[2]*0.5,
+ 0, 0.5*view[3], 0, view[1]+view[3]*0.5,
+ 0, 0, 0.5, 0.5,
+ 0, 0, 0, 1);
+ return z.times(p).times(m);
+ }
+
}
projects / anneal.git / blobdiff