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libgeometry: add matrix minor and cofactor functions

--- a/sys/include/geometry.h

+++ b/sys/include/geometry.h

@@ -84,6 +84,8 @@

 void transposem(Matrix);

 double detm(Matrix);

 double tracem(Matrix);

+double minorm(Matrix, int, int);

+double cofactorm(Matrix, int, int);

 void adjm(Matrix);

 void invm(Matrix);

 Point2 xform(Point2, Matrix);

@@ -97,6 +99,8 @@

 void transposem3(Matrix3);

 double detm3(Matrix3);

 double tracem3(Matrix3);

+double minorm3(Matrix3, int, int);

+double cofactorm3(Matrix3, int, int);

 void adjm3(Matrix3);

 void invm3(Matrix3);

 Point3 xform3(Point3, Matrix3);

--- a/sys/man/2/geometry

+++ b/sys/man/2/geometry

@@ -1,6 +1,6 @@

 .TH GEOMETRY 2

 .SH NAME

-Flerp, fclamp, Pt2, Vec2, addpt2, subpt2, mulpt2, divpt2, lerp2, dotvec2, vec2len, normvec2, edgeptcmp, ptinpoly, Pt3, Vec3, addpt3, subpt3, mulpt3, divpt3, lerp3, dotvec3, crossvec3, vec3len, normvec3, identity, addm, subm, mulm, smulm, transposem, detm, tracem, adjm, invm, xform, identity3, addm3, subm3, mulm3, smulm3, transposem3, detm3, tracem3, adjm3, invm3, xform3, Quat, Quatvec, addq, subq, mulq, smulq, sdivq, dotq, invq, qlen, normq, slerp, qrotate, rframexform, rframexform3, invrframexform, invrframexform3, centroid, barycoords, centroid3, vfmt, Vfmt, GEOMfmtinstall \- computational geometry library

+Flerp, fclamp, Pt2, Vec2, addpt2, subpt2, mulpt2, divpt2, lerp2, dotvec2, vec2len, normvec2, edgeptcmp, ptinpoly, Pt3, Vec3, addpt3, subpt3, mulpt3, divpt3, lerp3, dotvec3, crossvec3, vec3len, normvec3, identity, addm, subm, mulm, smulm, transposem, detm, tracem, minorm, cofactorm, adjm, invm, xform, identity3, addm3, subm3, mulm3, smulm3, transposem3, detm3, tracem3, minorm3, cofactorm3, adjm3, invm3, xform3, Quat, Quatvec, addq, subq, mulq, smulq, sdivq, dotq, invq, qlen, normq, slerp, qrotate, rframexform, rframexform3, invrframexform, invrframexform3, centroid, barycoords, centroid3, vfmt, Vfmt, GEOMfmtinstall \- computational geometry library

 .SH SYNOPSIS

 .de PB

 .PP

@@ -95,6 +95,8 @@

 void transposem(Matrix m);

 double detm(Matrix m);

 double tracem(Matrix m);

+double minorm(Matrix m, int row, int col);

+double cofactorm(Matrix m, int row, int col);

 void adjm(Matrix m);

 void invm(Matrix m);

 Point2 xform(Point2 p, Matrix m);

@@ -108,6 +110,8 @@

 void transposem3(Matrix3 m);

 double detm3(Matrix3 m);

 double tracem3(Matrix3 m);

+double minorm3(Matrix3 m, int row, int col);

+double cofactorm3(Matrix3 m, int row, int col);

 void adjm3(Matrix3 m);

 void invm3(Matrix3 m);

 Point3 xform3(Point3 p, Matrix3 m);

@@ -386,6 +390,16 @@

 .I m

 and returns the result.

 .TP

+.B minorm(\fIm\fP,\fIrow\fP,\fIcol\fP)

+Computes the minor of

+.I m

+and returns the result.

+.TP

+.B cofactorm(\fIm\fP,\fIrow\fP,\fIcol\fP)

+Computes the cofactor of

+.I m

+and returns the result.

+.TP

 .B adjm(\fIm\fP)

 Transforms the matrix

 .I m

@@ -451,6 +465,16 @@

 .TP

 .B tracem3(\fIm\fP)

 Computes the trace of

+.I m

+and returns the result.

+.TP

+.B minorm3(\fIm\fP,\fIrow\fP,\fIcol\fP)

+Computes the minor of

+.I m

+and returns the result.

+.TP

+.B cofactorm3(\fIm\fP,\fIrow\fP,\fIcol\fP)

+Computes the cofactor of

 .I m

 and returns the result.

 .TP

--- a/sys/src/libgeometry/matrix.c

+++ b/sys/src/libgeometry/matrix.c

@@ -84,6 +84,24 @@

 	return m[0][0] + m[1][1] + m[2][2];

 }

+double

+minorm(Matrix m, int row, int col)

+{

+	int i, j;

+	double subm[2][2];

+

+	for(i = 0; i < 3-1; i++)

+		for(j = 0; j < 3-1; j++)

+			subm[i][j] = m[i < row? i: i+1][j < col? j: j+1];

+	return subm[0][0]*subm[1][1] - subm[0][1]*subm[1][0];

+}

+

+double

+cofactorm(Matrix m, int row, int col)

+{

+	return minorm(m, row, col)*((row+col)&1 == 0? 1: -1);

+}

+

 void

 adjm(Matrix m)

 {

@@ -236,6 +254,25 @@

 tracem3(Matrix3 m)

 {

 	return m[0][0] + m[1][1] + m[2][2] + m[3][3];

+}

+

+double

+minorm3(Matrix3 m, int row, int col)

+{

+	int i, j;

+	Matrix subm;

+

+	memset(subm, 0, sizeof subm);

+	for(i = 0; i < 4-1; i++)

+		for(j = 0; j < 4-1; j++)

+			subm[i][j] = m[i < row? i: i+1][j < col? j: j+1];

+	return detm(subm);

+}

+

+double

+cofactorm3(Matrix3 m, int row, int col)

+{

+	return minorm3(m, row, col)*((row+col)&1 == 0? 1: -1);

 }

 void