standalone version release.

1 files changed, 348 insertions, 0 deletions

diff --git a/matrix.c b/matrix.c
new file mode 100644
index 0000000..d640403
--- /dev/null
+++ b/matrix.c
@@ -0,0 +1,348 @@
+#include <u.h>
+#include <libc.h>
+#include <geometry.h>
+
+/* 2D */
+
+void
+identity(Matrix m)
+{
+	memset(m, 0, 3*3*sizeof(double));
+	m[0][0] = m[1][1] = m[2][2] = 1;
+}
+
+void
+addm(Matrix a, Matrix b)
+{
+	int i, j;
+
+	for(i = 0; i < 3; i++)
+		for(j = 0; j < 3; j++)
+			a[i][j] += b[i][j];
+}
+
+void
+subm(Matrix a, Matrix b)
+{
+	int i, j;
+
+	for(i = 0; i < 3; i++)
+		for(j = 0; j < 3; j++)
+			a[i][j] -= b[i][j];
+}
+
+void
+mulm(Matrix a, Matrix b)
+{
+	int i, j, k;
+	Matrix tmp;
+
+	for(i = 0; i < 3; i++)
+		for(j = 0; j < 3; j++){
+			tmp[i][j] = 0;
+			for(k = 0; k < 3; k++)
+				tmp[i][j] += a[i][k]*b[k][j];
+		}
+	memmove(a, tmp, 3*3*sizeof(double));
+}
+
+void
+smulm(Matrix m, double s)
+{
+	int i, j;
+
+	for(i = 0; i < 3; i++)
+		for(j = 0; j < 3; j++)
+			m[i][j] *= s;
+}
+
+void
+transposem(Matrix m)
+{
+	int i, j;
+	double tmp;
+
+	for(i = 0; i < 3; i++)
+		for(j = i; j < 3; j++){
+			tmp = m[i][j];
+			m[i][j] = m[j][i];
+			m[j][i] = tmp;
+		}
+}
+
+double
+detm(Matrix m)
+{
+	return m[0][0]*(m[1][1]*m[2][2] - m[1][2]*m[2][1])+
+	       m[0][1]*(m[1][2]*m[2][0] - m[1][0]*m[2][2])+
+	       m[0][2]*(m[1][0]*m[2][1] - m[1][1]*m[2][0]);
+}
+
+double
+tracem(Matrix m)
+{
+	return m[0][0] + m[1][1] + m[2][2];
+}
+
+void
+adjm(Matrix m)
+{
+	Matrix tmp;
+
+	tmp[0][0] =  m[1][1]*m[2][2] - m[1][2]*m[2][1];
+	tmp[0][1] = -m[0][1]*m[2][2] + m[0][2]*m[2][1];
+	tmp[0][2] =  m[0][1]*m[1][2] - m[0][2]*m[1][1];
+	tmp[1][0] = -m[1][0]*m[2][2] + m[1][2]*m[2][0];
+	tmp[1][1] =  m[0][0]*m[2][2] - m[0][2]*m[2][0];
+	tmp[1][2] = -m[0][0]*m[1][2] + m[0][2]*m[1][0];
+	tmp[2][0] =  m[1][0]*m[2][1] - m[1][1]*m[2][0];
+	tmp[2][1] = -m[0][0]*m[2][1] + m[0][1]*m[2][0];
+	tmp[2][2] =  m[0][0]*m[1][1] - m[0][1]*m[1][0];
+	memmove(m, tmp, 3*3*sizeof(double));
+}
+
+/* Cayley-Hamilton */
+//void
+//invertm(Matrix m)
+//{
+//	Matrix m², r;
+//	double det, trm, trm²;
+//
+//	det = detm(m);
+//	if(det == 0)
+//		return;
+//	trm = tracem(m);
+//	memmove(m², m, 3*3*sizeof(double));
+//	mulm(m², m²);
+//	trm² = tracem(m²);
+//	identity(r);
+//	smulm(r, (trm*trm - trm²)/2);
+//	smulm(m, trm);
+//	subm(r, m);
+//	addm(r, m²);
+//	smulm(r, 1/det);
+//	memmove(m, r, 3*3*sizeof(double));
+//}
+
+/* Cramer's */
+void
+invm(Matrix m)
+{
+	double det;
+
+	det = detm(m);
+	if(det == 0)
+		return; /* singular matrices are not invertible */
+	adjm(m);
+	smulm(m, 1/det);
+}
+
+Point2
+xform(Point2 p, Matrix m)
+{
+	return (Point2){
+		p.x*m[0][0] + p.y*m[0][1] + p.w*m[0][2],
+		p.x*m[1][0] + p.y*m[1][1] + p.w*m[1][2],
+		p.x*m[2][0] + p.y*m[2][1] + p.w*m[2][2]
+	};
+}
+
+/* 3D */
+
+void
+identity3(Matrix3 m)
+{
+	memset(m, 0, 4*4*sizeof(double));
+	m[0][0] = m[1][1] = m[2][2] = m[3][3] = 1;
+}
+
+void
+addm3(Matrix3 a, Matrix3 b)
+{
+	int i, j;
+
+	for(i = 0; i < 4; i++)
+		for(j = 0; j < 4; j++)
+			a[i][j] += b[i][j];
+}
+
+void
+subm3(Matrix3 a, Matrix3 b)
+{
+	int i, j;
+
+	for(i = 0; i < 4; i++)
+		for(j = 0; j < 4; j++)
+			a[i][j] -= b[i][j];
+}
+
+void
+mulm3(Matrix3 a, Matrix3 b)
+{
+	int i, j, k;
+	Matrix3 tmp;
+
+	for(i = 0; i < 4; i++)
+		for(j = 0; j < 4; j++){
+			tmp[i][j] = 0;
+			for(k = 0; k < 4; k++)
+				tmp[i][j] += a[i][k]*b[k][j];
+		}
+	memmove(a, tmp, 4*4*sizeof(double));
+}
+
+void
+smulm3(Matrix3 m, double s)
+{
+	int i, j;
+
+	for(i = 0; i < 4; i++)
+		for(j = 0; j < 4; j++)
+			m[i][j] *= s;
+}
+
+void
+transposem3(Matrix3 m)
+{
+	int i, j;
+	double tmp;
+
+	for(i = 0; i < 4; i++)
+		for(j = i; j < 4; j++){
+			tmp = m[i][j];
+			m[i][j] = m[j][i];
+			m[j][i] = tmp;
+		}
+}
+
+double
+detm3(Matrix3 m)
+{
+	return m[0][0]*(m[1][1]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
+			m[1][2]*(m[2][3]*m[3][1] - m[2][1]*m[3][3])+
+			m[1][3]*(m[2][1]*m[3][2] - m[2][2]*m[3][1]))
+	      -m[0][1]*(m[1][0]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
+			m[1][2]*(m[2][3]*m[3][0] - m[2][0]*m[3][3])+
+			m[1][3]*(m[2][0]*m[3][2] - m[2][2]*m[3][0]))
+	      +m[0][2]*(m[1][0]*(m[2][1]*m[3][3] - m[2][3]*m[3][1])+
+			m[1][1]*(m[2][3]*m[3][0] - m[2][0]*m[3][3])+
+			m[1][3]*(m[2][0]*m[3][1] - m[2][1]*m[3][0]))
+	      -m[0][3]*(m[1][0]*(m[2][1]*m[3][2] - m[2][2]*m[3][1])+
+			m[1][1]*(m[2][2]*m[3][0] - m[2][0]*m[3][2])+
+			m[1][2]*(m[2][0]*m[3][1] - m[2][1]*m[3][0]));
+}
+
+double
+tracem3(Matrix3 m)
+{
+	return m[0][0] + m[1][1] + m[2][2] + m[3][3];
+}
+
+void
+adjm3(Matrix3 m)
+{
+	Matrix3 tmp;
+
+	tmp[0][0]=m[1][1]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
+		  m[2][1]*(m[1][3]*m[3][2] - m[1][2]*m[3][3])+
+		  m[3][1]*(m[1][2]*m[2][3] - m[1][3]*m[2][2]);
+	tmp[0][1]=m[0][1]*(m[2][3]*m[3][2] - m[2][2]*m[3][3])+
+		  m[2][1]*(m[0][2]*m[3][3] - m[0][3]*m[3][2])+
+		  m[3][1]*(m[0][3]*m[2][2] - m[0][2]*m[2][3]);
+	tmp[0][2]=m[0][1]*(m[1][2]*m[3][3] - m[1][3]*m[3][2])+
+		  m[1][1]*(m[0][3]*m[3][2] - m[0][2]*m[3][3])+
+		  m[3][1]*(m[0][2]*m[1][3] - m[0][3]*m[1][2]);
+	tmp[0][3]=m[0][1]*(m[1][3]*m[2][2] - m[1][2]*m[2][3])+
+		  m[1][1]*(m[0][2]*m[2][3] - m[0][3]*m[2][2])+
+		  m[2][1]*(m[0][3]*m[1][2] - m[0][2]*m[1][3]);
+	tmp[1][0]=m[1][0]*(m[2][3]*m[3][2] - m[2][2]*m[3][3])+
+		  m[2][0]*(m[1][2]*m[3][3] - m[1][3]*m[3][2])+
+		  m[3][0]*(m[1][3]*m[2][2] - m[1][2]*m[2][3]);
+	tmp[1][1]=m[0][0]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
+		  m[2][0]*(m[0][3]*m[3][2] - m[0][2]*m[3][3])+
+		  m[3][0]*(m[0][2]*m[2][3] - m[0][3]*m[2][2]);
+	tmp[1][2]=m[0][0]*(m[1][3]*m[3][2] - m[1][2]*m[3][3])+
+		  m[1][0]*(m[0][2]*m[3][3] - m[0][3]*m[3][2])+
+		  m[3][0]*(m[0][3]*m[1][2] - m[0][2]*m[1][3]);
+	tmp[1][3]=m[0][0]*(m[1][2]*m[2][3] - m[1][3]*m[2][2])+
+		  m[1][0]*(m[0][3]*m[2][2] - m[0][2]*m[2][3])+
+		  m[2][0]*(m[0][2]*m[1][3] - m[0][3]*m[1][2]);
+	tmp[2][0]=m[1][0]*(m[2][1]*m[3][3] - m[2][3]*m[3][1])+
+		  m[2][0]*(m[1][3]*m[3][1] - m[1][1]*m[3][3])+
+		  m[3][0]*(m[1][1]*m[2][3] - m[1][3]*m[2][1]);
+	tmp[2][1]=m[0][0]*(m[2][3]*m[3][1] - m[2][1]*m[3][3])+
+		  m[2][0]*(m[0][1]*m[3][3] - m[0][3]*m[3][1])+
+		  m[3][0]*(m[0][3]*m[2][1] - m[0][1]*m[2][3]);
+	tmp[2][2]=m[0][0]*(m[1][1]*m[3][3] - m[1][3]*m[3][1])+
+		  m[1][0]*(m[0][3]*m[3][1] - m[0][1]*m[3][3])+
+		  m[3][0]*(m[0][1]*m[1][3] - m[0][3]*m[1][1]);
+	tmp[2][3]=m[0][0]*(m[1][3]*m[2][1] - m[1][1]*m[2][3])+
+		  m[1][0]*(m[0][1]*m[2][3] - m[0][3]*m[2][1])+
+		  m[2][0]*(m[0][3]*m[1][1] - m[0][1]*m[1][3]);
+	tmp[3][0]=m[1][0]*(m[2][2]*m[3][1] - m[2][1]*m[3][2])+
+		  m[2][0]*(m[1][1]*m[3][2] - m[1][2]*m[3][1])+
+		  m[3][0]*(m[1][2]*m[2][1] - m[1][1]*m[2][2]);
+	tmp[3][1]=m[0][0]*(m[2][1]*m[3][2] - m[2][2]*m[3][1])+
+		  m[2][0]*(m[0][2]*m[3][1] - m[0][1]*m[3][2])+
+		  m[3][0]*(m[0][1]*m[2][2] - m[0][2]*m[2][1]);
+	tmp[3][2]=m[0][0]*(m[1][2]*m[3][1] - m[1][1]*m[3][2])+
+		  m[1][0]*(m[0][1]*m[3][2] - m[0][2]*m[3][1])+
+		  m[3][0]*(m[0][2]*m[1][1] - m[0][1]*m[1][2]);
+	tmp[3][3]=m[0][0]*(m[1][1]*m[2][2] - m[1][2]*m[2][1])+
+		  m[1][0]*(m[0][2]*m[2][1] - m[0][1]*m[2][2])+
+		  m[2][0]*(m[0][1]*m[1][2] - m[0][2]*m[1][1]);
+	memmove(m, tmp, 4*4*sizeof(double));
+}
+
+/* Cayley-Hamilton */
+//void
+//invertm3(Matrix3 m)
+//{
+//	Matrix3 m², m³, r;
+//	double det, trm, trm², trm³;
+//
+//	det = detm3(m);
+//	if(det == 0)
+//		return;
+//	trm = tracem3(m);
+//	memmove(m³, m, 4*4*sizeof(double));
+//	mulm(m³, m³);
+//	mulm(m³, m);
+//	trm³ = tracem3(m³);
+//	memmove(m², m, 4*4*sizeof(double));
+//	mulm(m², m²);
+//	trm² = tracem3(m²);
+//	identity3(r);
+//	smulm3(r, (trm*trm*trm - 3*trm*trm² + 2*trm³)/6);
+//	smulm3(m, (trm*trm - trm²)/2);
+//	smulm3(m², trm);
+//	subm(r, m);
+//	addm(r, m²);
+//	subm(r, m³);
+//	smulm(r, 1/det);
+//	memmove(m, r, 4*4*sizeof(double));
+//}
+
+/* Cramer's */
+void
+invm3(Matrix3 m)
+{
+	double det;
+
+	det = detm3(m);
+	if(det == 0)
+		return; /* singular matrices are not invertible */
+	adjm3(m);
+	smulm3(m, 1/det);
+}
+
+Point3
+xform3(Point3 p, Matrix3 m)
+{
+	return (Point3){
+		p.x*m[0][0] + p.y*m[0][1] + p.z*m[0][2] + p.w*m[0][3],
+		p.x*m[1][0] + p.y*m[1][1] + p.z*m[1][2] + p.w*m[1][3],
+		p.x*m[2][0] + p.y*m[2][1] + p.z*m[2][2] + p.w*m[2][3],
+		p.x*m[3][0] + p.y*m[3][1] + p.z*m[3][2] + p.w*m[3][3],
+	};
+}