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projectedSurfaceAreaMex.cpp
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projectedSurfaceAreaMex.cpp
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/*
* projectedSurfaceAreaMex.cpp
* Usage: s = projectedSurfaceAreaMex(angles, TRIV, X, Y, Z)
* Computes the projected surface area of s after a rotation.
* Variables:
* s - projected surface area.
* angles - input x, y, z rotation angles.
* TRIV - triangles of mesh.
* X - X coordinates of vertices.
* Y - Y coordinates of vertices.
* Z - Z coordinates of vertices.
*
* David Pickup 2013
*/
#include "mex.h"
#include <math.h>
// Define how to access arrays with two dimentions in matlab.
#define POS(x,y,M) (x + (y*M))
/* Multiply vertices by rotation matrix. */
void matrixMult(double *R, double *X, double *Y, double *Z, double *newX, double *newY, double *newZ, int nVerts)
{
// Iterate through all vertes.
for (int i = 0; i < nVerts; i++)
{
newX[i] = (R[POS(0,0,3)]*X[i]) + (R[POS(0,1,3)]*Y[i]) + (R[POS(0,2,3)]*Z[i]);
newY[i] = (R[POS(1,0,3)]*X[i]) + (R[POS(1,1,3)]*Y[i]) + (R[POS(1,2,3)]*Z[i]);
newZ[i] = (R[POS(2,0,3)]*X[i]) + (R[POS(2,1,3)]*Y[i]) + (R[POS(2,2,3)]*Z[i]);
}
}
/* Calculate the edge length between two 2D vertices. */
double edgeLength(double X1, double X2, double Y1, double Y2)
{
return sqrt(((Y1-X1)*(Y1-X1)) + ((Y2-X2)*(Y2-X2)));
}
/* Calculate the area of a 2D polygon from its vertices. */
double polyArea(double *X, double *Y, int nVerts)
{
// Initialise area.
double area = 0;
// The last vertex is the previous one of the first.
int j = nVerts - 1;
// Iterate through all vertices.
for (int i = 0; i < nVerts; i++)
{
// Accumulate the area.
area += (X[j]+X[i]) * (Y[j]-Y[i]);
// Set the previous vertex to the current.
j = i;
}
// Return the final area.
return area / 2;
}
/* Calculate the area of a 2D triangle using Heron's formula. */
double heron(double a, double b, double c)
{
return ((1/4) * sqrt((((a*a)+(b*b)+(c*c)) * ((a*a)+(b*b)+(c*c))) - (2*((a*a*a*a)+(b*b*b*b)+(c*c*c*c)))));
}
/* The matlab gateway function. */
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
// Varify that the correct number of function arguments have been given.
if (nrhs != 5)
mexErrMsgTxt("Five input arguments required.");
if (nlhs != 1)
mexErrMsgTxt("One output argument required.");
// Initialise variables.
double *TRIV; // Mesh triangles.
double *X; // X coordinates of vertices.
double *Y; // Y coordinates of vertices.
double *Z; // Z coordinates of vertices.
double *newX; // X coordinates of rotated vertices.
double *newY; // Y coordinates of rotated vertices.
double *newZ; // Z coordinates of rotated vertices.
double *tmpX; // temporary X coordinates used during rotation.
double *tmpY; // temporary Y coordinates used during rotation.
double *tmpZ; // temporary Z coordinates used during rotation.
double triX[3]; // X coordinates of single triangle.
double triY[3]; // Y coordinates of single triangle.
double triZ[3]; // Z coordinates of single triangle.
double *angles; // Rotation angles.
int m,n; // Size of TRIV.
double a,b,c; // Edge lengths.
// Get rotation angles.
angles = mxGetPr(prhs[0]);
//mexPrintf("Angles loaded.\n");
// Get triangles and vertex coordinates.
TRIV = mxGetPr(prhs[1]);
m = mxGetM(prhs[1]);
n = mxGetN(prhs[1]);
X = mxGetPr(prhs[2]);
Y = mxGetPr(prhs[3]);
Z = mxGetPr(prhs[4]);
int nVerts = mxGetM(prhs[2]);
newX = (double*) calloc(nVerts,sizeof(double));
newY = (double*) calloc(nVerts,sizeof(double));
newZ = (double*) calloc(nVerts,sizeof(double));
tmpX = (double*) calloc(nVerts,sizeof(double));
tmpY = (double*) calloc(nVerts,sizeof(double));
tmpZ = (double*) calloc(nVerts,sizeof(double));
//mexPrintf("Mesh loaded.\n");
// Create rotation matrices.
double Rx[] = {1, 0, 0, 0, cos(angles[0]), sin(angles[0]), 0, -sin(angles[0]), cos(angles[0])};
double Ry[] = {cos(angles[1]), 0, -sin(angles[1]), 0, 1, 0, sin(angles[1]), 0, cos(angles[1])};
double Rz[] = {cos(angles[2]), sin(angles[2]), 0, -sin(angles[2]), cos(angles[2]), 0, 0, 0, 1};
//mexPrintf("Created rotation vertices.\n");
// Rotate vertices.
matrixMult(Rx, X, Y, Z, newX, newY, newZ, mxGetM(prhs[2]));
matrixMult(Ry, newX, newY, newZ, tmpX, tmpY, tmpZ, mxGetM(prhs[2]));
matrixMult(Rz, tmpX, tmpY, tmpZ, newX, newY, newZ, mxGetM(prhs[2]));
//mexPrintf("Rotated vertices.\n");
// Initialise output value.
plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL);
double *r = mxGetPr(plhs[0]);
r[0] = 0;
//mexPrintf("Initialised output variable: %f.\n", r[0]);
// Iterate through all triangles.
for (int i = 0; i < m; i++)
{
// Get vertices for current triangle.
for (int j = 0; j < 3; j++)
{
triX[j] = newX[(int)TRIV[POS(i,j,m)]-1];
triY[j] = newY[(int)TRIV[POS(i,j,m)]-1];
triZ[j] = newZ[(int)TRIV[POS(i,j,m)]-1];
}
//mexPrintf("Got vertices for current triangle.\n");
//mexPrintf("Triangle %d of %d: (%f, %f, %f) (%f, %f, %f) (%f, %f, %f)\n", i, m,
// triX[0], triY[0], triZ[0],
// triX[1], triY[1], triZ[1],
// triX[2], triY[2], triZ[2]);
// Calculate projected area of current triangle and add to total.
a = polyArea(triX, triY, 3);
if (a < 0)
a = a * -1;
b = polyArea(triX, triZ, 3);
if (b < 0)
b = b * -1;
c = polyArea(triY, triZ, 3);
if (c < 0)
c = c * -1;
r[0] += a + b + c;
}
free(newX);
free(newY);
free(newZ);
free(tmpX);
free(tmpY);
free(tmpZ);
}