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catmullromspline.cpp
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catmullromspline.cpp
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/*
CSC 486 Summer 2014
Ryan Guy
*/
#include "catmullromspline.h"
#include <QtDebug>
CatmullRomSpline::CatmullRomSpline()
{
}
CatmullRomSpline::CatmullRomSpline(QVector<glm::vec4> &control_points):
controlPoints(control_points)
{
initializeGeometryVectors();
initializeBasisMatrix();
initializeSegmentLengths();
initializeArcLengthTable();
}
CatmullRomSpline::~CatmullRomSpline()
{
//delete &controlPoints;
}
void CatmullRomSpline::initializeGeometryVectors() {
// compute tangents
// A tangent of a point is computed as a factor of the vector
// starting at the point previous point and ending at the point's next point
glm::vec3 tangents[MAX_NUM_CONTROL_POINTS - 2];
for (int i=1; i < controlPoints.size() - 1; i++) {
glm::vec4 p1 = controlPoints[i-1];
glm::vec4 p2 = controlPoints[i+1];
float dx = 0.5f * (p2.x - p1.x);
float dy = 0.5f * (p2.y - p1.y);
float dz = 0.5f * (p2.z - p1.z);
tangents[i-1] = glm::vec3(dx, dy, dz);
}
// construct geomentry vectors
// Example: A geometry vector for the x component is in form:
// {p1x, p2x, t1x, t2x}
// where p1 and p2 are the start point and end point of a segment
// and t1 and t2 are their tangent vectors
for (int i=0; i < controlPoints.size() - 3; i++) {
glm::vec4 p1 = controlPoints[i + 1];
glm::vec4 p2 = controlPoints[i + 2];
glm::vec3 t1 = tangents[i];
glm::vec3 t2 = tangents[i + 1];
geometryVectorsX.append(glm::vec4(p1.x, p2.x, t1.x, t2.x));
geometryVectorsY.append(glm::vec4(p1.y, p2.y, t1.y, t2.y));
geometryVectorsZ.append(glm::vec4(p1.z, p2.z, t1.z, t2.z));
}
}
void CatmullRomSpline::initializeBasisMatrix() {
// System of equations for ax^3 + bx^2 + cx + d
// Example for x:
// x(0) = p0x = [0 0 0 1]*Cx // x component of p0
// x(1) = p3x = [1 1 1 1]*Cx // x component of p3
// x'(0) = t0x = [0 0 1 0]*Cx // tangent x component to p0
// x'(1) = t3x = [3 2 1 1]*Cx // tangent x component to p3
glm::mat4 invBasisMatrix = glm::mat4(glm::vec4(0.0f, 0.0f, 0.0f, 1.0f),
glm::vec4(1.0f, 1.0f, 1.0f, 1.0f),
glm::vec4(0.0f, 0.0f, 1.0f, 0.0f),
glm::vec4(3.0f, 2.0f, 1.0f, 0.0f));
// invert and transpose to get basis matrix
basisMatrix = glm::transpose(glm::inverse(invBasisMatrix));
}
glm::vec3 CatmullRomSpline::evaluatePointOnSegment(float t, int segmentIdx) {
glm::vec4 paramVect = glm::vec4(t*t*t, t*t, t, 1.0f);
glm::vec4 geomX = geometryVectorsX[segmentIdx];
glm::vec4 geomY = geometryVectorsY[segmentIdx];
glm::vec4 geomZ = geometryVectorsZ[segmentIdx];
// point = paramVect * basisMatrix * geometryVector
float x = glm::dot(paramVect, basisMatrix * geomX);
float y = glm::dot(paramVect, basisMatrix * geomY);
float z = glm::dot(paramVect, basisMatrix * geomZ);
return glm::vec3(x, y, z);
}
void CatmullRomSpline::initializeSegmentLengths() {
float totalLength = 0.0f;
float step = 1.0f / (POINTS_PER_SEGMENT - 1);
for (int segIdx=0; segIdx < controlPoints.size() - 3; segIdx++) {
// calculate length of a segment
float t = step;
float segLen = 0.0f;
glm::vec3 lastPoint = evaluatePointOnSegment(0.0f, segIdx);
for (int i=1; i < POINTS_PER_SEGMENT; i++) {
glm::vec3 p = evaluatePointOnSegment(t, segIdx);
float stepDist = glm::distance(p, lastPoint);
segLen += stepDist;
lastPoint = p;
t += step;
}
totalLength += segLen;
segmentLengths.append(segLen);
}
this->totalLength = totalLength;
}
void CatmullRomSpline::initializeArcLengthTable() {
float step = 1.0f / (POINTS_PER_SEGMENT - 1);
float currentLength = 0.0f;
for (int segIdx=0; segIdx < controlPoints.size() - 3; segIdx++) {
float t = step;
float segLen = 0.0f;
glm::vec3 lastPoint = evaluatePointOnSegment(0.0f, segIdx);
arcLengthTable.append(glm::vec3(currentLength, segIdx, 0.0f));
for (int i=1; i < POINTS_PER_SEGMENT; i++) {
glm::vec3 p = evaluatePointOnSegment(t, segIdx);
float stepDist = glm::distance(p, lastPoint);
segLen += stepDist;
currentLength += stepDist;
arcLengthTable.append(glm::vec3(currentLength, segIdx, t));
lastPoint = p;
t += step;
}
}
}
int CatmullRomSpline::getSegmentIndexAtArcLength(float len) {
float currentLength = 0.0f;
int i = 0;
for (i=0; i < segmentLengths.size(); i++) {
currentLength += segmentLengths[i];
if (len <= currentLength) {
return i;
}
}
return i-1;
}
glm::vec3 CatmullRomSpline::getPointAtArcLength(float len) {
int segIdx = getSegmentIndexAtArcLength(len);
int min = segIdx * POINTS_PER_SEGMENT;
int max = min + POINTS_PER_SEGMENT - 1;
for (int i=min; i < max; i++) {
glm::vec3 data2 = arcLengthTable[i+1];
if (len <= data2.x) {
glm::vec3 data1 = arcLengthTable[i];
float minLen = data1.x;
float maxLen = data2.x;
float minT = data1.z;
float maxT = data2.z;
float ratio = (len - minLen) / (maxLen - minLen);
float t = minT + ratio * (maxT - minT);
return evaluatePointOnSegment(t, segIdx);
}
}
// last control point
glm::vec4 p = controlPoints[controlPoints.size()-2];
return glm::vec3(p.x, p.y, p.z);
}
glm::vec3 CatmullRomSpline::interpolateForT(float t) {
if (t < 0.0f) {
t = 0.0f;
} else if ( t > 1.0f) {
t = 1.0f;
}
return getPointAtArcLength(t * totalLength);
}