void minimum_area_enclosing_rectangle(
const Polygon2d& PP,
vec2& S, vec2& T
) {
// Note: this implementation has O(n2) complexity :-(
// (where n is the number of vertices in the convex hull)
// If this appears to be a bottleneck, use a smarter
// implementation with better complexity.
Polygon2d P ;
convex_hull(PP, P) ;
int N = P.size() ;
// Add the first vertex at the end of P
P.push_back(P[0]) ;
double min_area = Numeric::big_double ;
for(int i=1; i<=N; i++) {
vec2 Si = P[i] - P[i-1] ;
if( ( Si.length2() ) < 1e-20) {
continue ;
}
vec2 Ti(-Si.y, Si.x) ;
normalize(Si) ;
normalize(Ti) ;
double s0 = Numeric::big_double ;
double s1 = -Numeric::big_double ;
double t0 = Numeric::big_double ;
double t1 = -Numeric::big_double ;
for(int j=1; j<N; j++) {
vec2 D = P[j] - P[0] ;
double s = dot(Si, D) ;
s0 = gx_min(s0, s) ;
s1 = gx_max(s1, s) ;
double t = dot(Ti, D) ;
t0 = gx_min(t0, t) ;
t1 = gx_max(t1, t) ;
}
double area = (s1 - s0) * (t1 - t0) ;
if(area < min_area) {
min_area = area ;
if((s1 - s0) < (t1 - t0)) {
S = Si ;
T = Ti ;
} else {
S = Ti ;
T = Si ;
}
}
}
}
size_t SparseMatrixPatternCRS::bandwidth() const {
size_t result = 0 ;
for(index_t i=0; i<m(); i++) {
for(index_t jj=rowptr[i]; jj < rowptr[i+1]; jj++) {
index_t j = colind[jj] ;
result = gx_max(result, (size_t)gx_abs(signed_index_t(i) - signed_index_t(j))) ;
}
}
return result ;
}
signed_index_t SparseMatrixPatternCRS::find_furthest_node(index_t x, IndexArray& dist) {
std::deque<index_t> Q ;
for(index_t i=0; i<m(); i++) { dist[i] = NO_INDEX ; }
index_t r = x ; index_t ex = 0 ; size_t dr = row_nnz(r) ;
dist[x] = 0 ;
Q.push_back(x) ;
while(!Q.empty()) {
index_t cur = Q.front() ;
Q.pop_front() ;
if(dist[cur] > ex) {
r = cur ; dr = row_nnz(r) ; ex = dist[r] ;
} else if(dist[cur] == ex) {
size_t d = row_nnz(cur) ;
if(d < dr) { r = cur ; dr = d ; }
}
for(index_t jj=rowptr[cur]; jj < rowptr[cur+1]; jj++) {
index_t j = colind[jj] ;
if(dist[j] == NO_INDEX) {
dist[j] = dist[cur] + 1 ;
Q.push_back(j) ;
}
}
}
size_t er = 0 ;
for(index_t i=0; i<m(); i++) { dist[i] = NO_INDEX ; }
dist[r] = 0 ;
Q.push_back(r) ;
while(!Q.empty()) {
index_t cur = Q.front() ;
Q.pop_front() ;
for(index_t jj=rowptr[cur]; jj < rowptr[cur+1]; jj++) {
index_t j = colind[jj] ;
if(dist[j] == NO_INDEX) {
dist[j] = dist[cur] + 1 ;
er = gx_max(er, dist[j]) ;
Q.push_back(j) ;
}
}
}
std::cerr << " ex = " << ex << " er = " << er << std::endl ;
return (er > ex) ? signed_index_t(r) : -1 ;
}
void begin_spheres() {
if(sphere_vertex_program_id == 0 && sphere_fragment_program_id == 0) {
create_sphere_programs() ;
}
glDisable(GL_NORMALIZE) ;
glEnable(GL_VERTEX_PROGRAM_ARB) ;
glEnable(GL_VERTEX_PROGRAM_POINT_SIZE_ARB) ;
glBindProgramARB(GL_VERTEX_PROGRAM_ARB, sphere_vertex_program_id) ;
glEnable(GL_FRAGMENT_PROGRAM_ARB) ;
glBindProgramARB(GL_FRAGMENT_PROGRAM_ARB, sphere_fragment_program_id) ;
// For the moment, this is the only way we have to find the
// dimension of the OpenGL window.
float w=float(screen_w), h=float(screen_h), r=gx_max(w,h) ;
glProgramLocalParameter4dARB(GL_VERTEX_PROGRAM_ARB, 0, 1.0/r, 0, 0, 0.2) ;
glProgramLocalParameter4dARB(GL_FRAGMENT_PROGRAM_ARB, 0, -w/2.0, -h/2.0, 0, 0) ;
glProgramLocalParameter4dARB(GL_FRAGMENT_PROGRAM_ARB, 1, -2.0/r, -2.0/r, 0, 0) ;
glBegin(GL_POINTS) ;
}