bool KoConnectionShapePrivate::intersects(const QPointF &p1, const QPointF &d1, const QPointF &p2, const QPointF &d2, QPointF &isect)
{
qreal sp1 = scalarProd(d1, p2 - p1);
if (sp1 < 0.0)
return false;
qreal sp2 = scalarProd(d2, p1 - p2);
if (sp2 < 0.0)
return false;
// use cross product to check if rays intersects at all
qreal cp = crossProd(d1, d2);
if (cp == 0.0) {
// rays are parallel or coincidient
if (p1.x() == p2.x() && d1.x() == 0.0 && d1.y() != d2.y()) {
// vertical, coincident
isect = 0.5 * (p1 + p2);
} else if (p1.y() == p2.y() && d1.y() == 0.0 && d1.x() != d2.x()) {
// horizontal, coincident
isect = 0.5 * (p1 + p2);
} else {
return false;
}
} else {
// they are intersecting normally
isect = p1 + sp1 * d1;
}
return true;
}
int main(int argc, char** argv) {
if(argc != 3) {
printf("Usage: ./gram_schmidt vector_length number_of_vectors\n");
exit(EXIT_FAILURE);
}
double** v;
double **q;
double temp_norm, sigma;
int row = atoi(argv[1]);
//int col = row;
int col = atoi(argv[2]);
if(row < col) {
printf("It is not possible to create an orthogonal base with such values. \n");
exit(-1);
}
int k,i,j,ttime;
v = alloc_matrix(row, col);
q = alloc_matrix(row, col);
// initializes v with random values
srand(time(NULL));
init(v, row, col);
// compute
ttime=timer();
for(i=0; i<row; i++) {
temp_norm = vecNorm(v[i],col);
for (k=0; k<col; k++)
q[i][k] = v[i][k]/temp_norm;
#pragma omp parallel for private(temp_norm, k, j, sigma) schedule(dynamic)
for(j=i+1; j<row; j++) {
sigma = scalarProd(q[i], v[j], col);
for(k=0; k<col; k++)
v[j][k] -=sigma*q[i][k];
}
}
ttime=timer()-ttime;
printf("Time: %f \n",ttime/1000000.0);
printf("Check orthogonality: %e \n",scalarProd(q[col/2], q[col/3], row));
}
QPointF KoConnectionShapePrivate::perpendicularDirection(const QPointF &p1, const QPointF &d1, const QPointF &p2)
{
QPointF perpendicular(d1.y(), -d1.x());
qreal sp = scalarProd(perpendicular, p2 - p1);
if (sp < 0.0)
perpendicular *= -1.0;
return perpendicular;
}
void KoConnectionShapePrivate::normalPath(const qreal MinimumEscapeLength)
{
// Clear the path to build it again.
path.clear();
path.append(handles[KoConnectionShape::StartHandle]);
QList<QPointF> edges1;
QList<QPointF> edges2;
QPointF direction1 = escapeDirection(KoConnectionShape::StartHandle);
QPointF direction2 = escapeDirection(KoConnectionShape::EndHandle);
QPointF edgePoint1 = handles[KoConnectionShape::StartHandle] + MinimumEscapeLength * direction1;
QPointF edgePoint2 = handles[KoConnectionShape::EndHandle] + MinimumEscapeLength * direction2;
edges1.append(edgePoint1);
edges2.prepend(edgePoint2);
if (handleConnected(KoConnectionShape::StartHandle) && handleConnected(KoConnectionShape::EndHandle)) {
QPointF intersection;
bool connected = false;
do {
// first check if directions from current edge points intersect
if (intersects(edgePoint1, direction1, edgePoint2, direction2, intersection)) {
// directions intersect, we have another edge point and be done
edges1.append(intersection);
break;
}
// check if we are going toward the other handle
qreal sp = scalarProd(direction1, edgePoint2 - edgePoint1);
if (sp >= 0.0) {
// if we are having the same direction, go all the way toward
// the other handle, else only go half the way
if (direction1 == direction2)
edgePoint1 += sp * direction1;
else
edgePoint1 += 0.5 * sp * direction1;
edges1.append(edgePoint1);
// switch direction
direction1 = perpendicularDirection(edgePoint1, direction1, edgePoint2);
} else {
// we are not going into the same direction, so switch direction
direction1 = perpendicularDirection(edgePoint1, direction1, edgePoint2);
}
} while (! connected);
}
path.append(edges1);
path.append(edges2);
path.append(handles[KoConnectionShape::EndHandle]);
}
void inline collSpherePlanes()
{
// p= startpunkt
// q=endpunkt
// a,b,c = Dreieckspunkte
// u,v,w baryzentrische koordinaten zum Schnittpunkt s
// s = u*a + v*b + w*c
triangle tri;
bowl *b;
float u,v,w;
int check = 0;
Vector s(3); // schnittpunkt mit dreieck
float pace = 0;
float lambda = 0;
for(int h = 0; h < bcount; h++)
{
b = &bowls[h];
if(b->fixed)
{
continue;
}
for(int i = 0; i < objects.size(); i++)
{
for(int j = 0; j < objects[i].triangles.size(); j++)
{
Vector dir(3);
dir[0] = b->pace[0];
dir[1] = b->pace[1];
dir[2] = b->pace[2];
normalizeVector(&dir);
float len = getVectorLen(dir);
tri = objects[i].triangles[j];
// tri um länge des radius heranholen
float sign = (scalarProd(&dir, &tri.normal) < 0) ? 1 : -1;
tri.a[0] += b->radius*tri.normal[0]*sign;
tri.a[1] += b->radius*tri.normal[1]*sign;
tri.a[2] += b->radius*tri.normal[2]*sign;
tri.b[0] += b->radius*tri.normal[0]*sign;
tri.b[1] += b->radius*tri.normal[1]*sign;
tri.b[2] += b->radius*tri.normal[2]*sign;
tri.c[0] += b->radius*tri.normal[0]*sign;
tri.c[1] += b->radius*tri.normal[1]*sign;
tri.c[2] += b->radius*tri.normal[2]*sign;
// broad phase:
pace = getVectorLen(b->pace);
// naiver test mit unendlicher ebene
check = checkIntersectRayPlane(&tri, &b->oldPos, &b->pace, &lambda);
if (check == 0 || lambda > pace)
{
continue;
}
std::cout << lambda << "\r\n";
//check = IntersectLineTriangle(b->oldPos, b->pos, tri.a, tri.b, tri.c, u,v,w, &tri);
s[0] = b->oldPos[0] + lambda*dir[0];
s[1] = b->oldPos[1] + lambda*dir[1];
s[2] = b->oldPos[2] + lambda*dir[2];
check = checkPointInTriangle(s, &tri);
Vector face = s - b->oldPos;
normalizeVector(&face);
float dot = scalarProd(&face, &dir);
if(check == 1 && dot > 0)
{
// schauen, ob schnittpunkt überschritten wurde
if(lambda <= pace)
{
Vector m(3);
m[0] = b->oldPos[0] + b->pace[0]/2;
m[1] = b->oldPos[1] + b->pace[1]/2;
m[2] = b->oldPos[2] + b->pace[2]/2;
// schauen, ob schnittpunkt im radius ist
float d = getDistance(s,m);
if(d < pace)
{
// kollision
Vector out(3);
float subLen = abs(getDistance(s, b->pos));
getOutVector(dir, tri.normal, &out);
b->pos[0] = s[0] + subLen * out[0]; // + out[0] * subLen;
b->pos[1] = s[1] + subLen * out[1]; // + out[1] * subLen;
b->pos[2] = s[2] + subLen * out[2]; // + out[2] * subLen;
// neue schrittweite
// gleitanteil
Vector slide = out - tri.normal;
float outDotN = abs(scalarProd(&out,&tri.normal));
slide[0]= (out[0] - outDotN*tri.normal[0]);
slide[1]= (out[1] - outDotN*tri.normal[1]);
slide[2]= (out[2] - outDotN*tri.normal[2]);
out[0] = tri.normal[0] + 8*slide[0];
out[1] = tri.normal[1] + 8*slide[1];
out[2] = tri.normal[2] + 8*slide[2];
normalizeVector(&out);
// kugel fällt durch das mesh durch, wenn aktiviert
if(friction)
{
pace *= b->friction;
}
if(pace <= 0.001 && fix)
{
pace = 0;
b->fixed = true;
}
b->pace[0] = out[0] * pace;
b->pace[1] = out[1] * pace;
b->pace[2] = out[2] * pace;
}
}
}
}
}
}
}
//derivative of activation function 1/(cosh(x)^2)
double fdx(Neuron* neuron, double* in) {
return 1 / pow(cosh(scalarProd(neuron->w, in, N)), 2);
}
//activation function
double f(Neuron* neuron, double* in) {
return tanh(scalarProd(neuron->w, in, N));
}