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+/*
+ algebra.cpp: This file contains a number of utilities useful for handling
+ 3D vectors
+
+ This work is an adaptation from vvector.h, written by Linas Vepstras. The
+ original code can be found at:
+
+ https://github.com/markkilgard/glut/blob/master/lib/gle/vvector.h
+
+ HISTORY:
+ Written by Linas Vepstas, August 1991
+ Added 2D code, March 1993
+ Added Outer products, C++ proofed, Linas Vepstas October 1993
+ Adapted for altitude estimation tasks by Juan Gallostra June 2018
+*/
+
+//#include <cmath>
+#include <stdio.h>
+
+#include "algebra.h"
+
+// Copy 3D vector
+void copyVector(float b[3],float a[3])
+{
+ b[0] = a[0];
+ b[1] = a[1];
+ b[2] = a[2];
+}
+
+
+// Vector difference
+void subtractVectors(float v21[3], float v2[3], float v1[3])
+{
+ v21[0] = v2[0] - v1[0];
+ v21[1] = v2[1] - v1[1];
+ v21[2] = v2[2] - v1[2];
+}
+
+// Vector sum
+void sumVectors(float v21[3], float v2[3], float v1[3])
+{
+ v21[0] = v2[0] + v1[0];
+ v21[1] = v2[1] + v1[1];
+ v21[2] = v2[2] + v1[2];
+}
+
+// scalar times vector
+void scaleVector(float c[3],float a, float b[3])
+{
+ (c)[0] = a*b[0];
+ (c)[1] = a*b[1];
+ (c)[2] = a*b[2];
+}
+
+// accumulate scaled vector
+void accumulateScaledVector(float c[3], float a, float b[3])
+{
+ (c)[0] += a*b[0];
+ (c)[1] += a*b[1];
+ (c)[2] += a*b[2];
+}
+
+// Vector dot product
+void dotProductVectors(float * c, float a[3], float b[3])
+{
+ *c = a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
+}
+
+// Vector length
+void vectorLength(float * len, float a[3])
+{
+ float tmp;
+ tmp = a[0]*a[0] + a[1]*a[1]+a[2]*a[2];
+ *len = sqrt(tmp);
+}
+
+// Normalize vector
+void normalizeVector(float a[3])
+{
+ float len;
+ vectorLength(& len,a);
+ if (len != 0.0) {
+ len = 1.0 / len;
+ a[0] *= len;
+ a[1] *= len;
+ a[2] *= len;
+ }
+}
+
+// 3D Vector cross product yeilding vector
+void crossProductVectors(float c[3], float a[3], float b[3])
+{
+ c[0] = a[1] * b[2] - a[2] * b[1];
+ c[1] = a[2] * b[0] - a[0] * b[2];
+ c[2] = a[0] * b[1] - a[1] * b[0];
+}
+
+// initialize matrix
+void identityMatrix3x3(float m[3][3])
+{
+ m[0][0] = 1.0;
+ m[0][1] = 0.0;
+ m[0][2] = 0.0;
+
+ m[1][0] = 0.0;
+ m[1][1] = 1.0;
+ m[1][2] = 0.0;
+
+ m[2][0] = 0.0;
+ m[2][1] = 0.0;
+ m[2][2] = 1.0;
+}
+
+// matrix copy
+void copyMatrix3x3(float b[3][3], float a[3][3])
+{
+ b[0][0] = a[0][0];
+ b[0][1] = a[0][1];
+ b[0][2] = a[0][2];
+
+ b[1][0] = a[1][0];
+ b[1][1] = a[1][1];
+ b[1][2] = a[1][2];
+
+ b[2][0] = a[2][0];
+ b[2][1] = a[2][1];
+ b[2][2] = a[2][2];
+}
+
+// matrix transpose
+void transposeMatrix3x3(float b[3][3], float a[3][3])
+{
+ b[0][0] = a[0][0];
+ b[0][1] = a[1][0];
+ b[0][2] = a[2][0];
+
+ b[1][0] = a[0][1];
+ b[1][1] = a[1][1];
+ b[1][2] = a[2][1];
+
+ b[2][0] = a[0][2];
+ b[2][1] = a[1][2];
+ b[2][2] = a[2][2];
+}
+
+// multiply matrix by scalar
+void scaleMatrix3x3(float b[3][3], float s, float a[3][3])
+{
+ b[0][0] = (s) * a[0][0];
+ b[0][1] = (s) * a[0][1];
+ b[0][2] = (s) * a[0][2];
+
+ b[1][0] = (s) * a[1][0];
+ b[1][1] = (s) * a[1][1];
+ b[1][2] = (s) * a[1][2];
+
+ b[2][0] = (s) * a[2][0];
+ b[2][1] = (s) * a[2][1];
+ b[2][2] = (s) * a[2][2];
+}
+
+// multiply matrix by scalar and add result to another matrix
+void scaleAndAccumulateMatrix3x3(float b[3][3], float s, float a[3][3])
+{
+ b[0][0] += s * a[0][0];
+ b[0][1] += s * a[0][1];
+ b[0][2] += s * a[0][2];
+
+ b[1][0] += s * a[1][0];
+ b[1][1] += s * a[1][1];
+ b[1][2] += s * a[1][2];
+
+ b[2][0] += s * a[2][0];
+ b[2][1] += s * a[2][1];
+ b[2][2] += s * a[2][2];
+}
+
+// matrix product
+// c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y]
+void matrixProduct3x3(float c[3][3], float a[3][3], float b[3][3])
+{
+ c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0];
+ c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1];
+ c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2];
+
+ c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0];
+ c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1];
+ c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2];
+
+ c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0];
+ c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1];
+ c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2];
+}
+
+// matrix times vector
+void matrixDotVector3x3(float p[3], float m[3][3], float v[3])
+{
+ p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
+ p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
+ p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
+}
+
+// determinant of matrix
+// Computes determinant of matrix m, returning d
+void determinant3x3(float * d, float m[3][3])
+{
+ *d = m[0][0] * (m[1][1]*m[2][2] - m[1][2] * m[2][1]);
+ *d -= m[0][1] * (m[1][0]*m[2][2] - m[1][2] * m[2][0]);
+ *d += m[0][2] * (m[1][0]*m[2][1] - m[1][1] * m[2][0]);
+}
+
+// adjoint of matrix
+// Computes adjoint of matrix m, returning a
+// (Note that adjoint is just the transpose of the cofactor matrix)
+void adjoint3x3(float a[3][3], float m[3][3])
+{
+ a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1];
+ a[1][0] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]);
+ a[2][0] = m[1][0]*m[2][1] - m[1][1]*m[2][0];
+ a[0][1] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]);
+ a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0];
+ a[2][1] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]);
+ a[0][2] = m[0][1]*m[1][2] - m[0][2]*m[1][1];
+ a[1][2] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]);
+ a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0];
+}
+
+// compute adjoint of matrix and scale
+// Computes adjoint of matrix m, scales it by s, returning a
+void scaleAdjoint3x3(float a[3][3], float s, float m[3][3])
+{
+ a[0][0] = (s) * (m[1][1] * m[2][2] - m[1][2] * m[2][1]);
+ a[1][0] = (s) * (m[1][2] * m[2][0] - m[1][0] * m[2][2]);
+ a[2][0] = (s) * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
+
+ a[0][1] = (s) * (m[0][2] * m[2][1] - m[0][1] * m[2][2]);
+ a[1][1] = (s) * (m[0][0] * m[2][2] - m[0][2] * m[2][0]);
+ a[2][1] = (s) * (m[0][1] * m[2][0] - m[0][0] * m[2][1]);
+
+ a[0][2] = (s) * (m[0][1] * m[1][2] - m[0][2] * m[1][1]);
+ a[1][2] = (s) * (m[0][2] * m[1][0] - m[0][0] * m[1][2]);
+ a[2][2] = (s) * (m[0][0] * m[1][1] - m[0][1] * m[1][0]);
+}
+
+// inverse of matrix
+// Compute inverse of matrix a, returning determinant m and
+// inverse b
+void invert3x3(float b[3][3], float a[3][3])
+{
+ float tmp;
+ determinant3x3(& tmp, a);
+ tmp = 1.0 / (tmp);
+ scaleAdjoint3x3(b, tmp, a);
+}
+
+// skew matrix from vector
+void skew(float a[3][3], float v[3])
+{
+ a[0][1] = -v[2];
+ a[0][2] = v[1];
+ a[1][2] = -v[0];
+ a[1][0] = v[2];
+ a[2][0] = -v[1];
+ a[2][1] = v[0];
+ // set diagonal to 0
+ a[0][0] = 0.0;
+ a[1][1] = 0.0;
+ a[2][2] = 0.0;
+}
+
+void printMatrix3X3(float mmm[3][3])
+{
+ int i,j;
+ printf ("matrix mmm is \n");
+ if (mmm == NULL) {
+ printf (" Null \n");
+ } else {
+ for (i=0; i<3; i++) {
+ for (j=0; j<3; j++) {
+ printf ("%f ", mmm[i][j]);
+ }
+ printf (" \n");
+ }
+ }
+}
+
+void vecPrint(float a[3])
+{
+ float len;
+ vectorLength(& len, a);
+ printf(" a is %f %f %f length of a is %f \n", a[0], a[1], a[2], len);
+}
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