gdouble triangle_circumcircle_radius( Point2 *p1, Point2 *p2, Point2 *p3 )
{
return triangle_circumcircle_radius_edge_length(
point2_distance(p1,p2),
point2_distance(p2,p3),
point2_distance(p3,p1) );
}
gdouble triangle_area( const Point2 *p1, const Point2 *p2, const Point2 *p3 )
{
gdouble l1 = point2_distance( p1, p2 );
gdouble l2 = point2_distance( p2, p3 );
gdouble l3 = point2_distance( p3, p1 );
gdouble s = 0.5*( l1 + l2 + l3 );
return sqrt( s*( s-l1 )*( s-l2 )*( s-l3 ) );
}
void element_edge_lengths( const Element *element,
gdouble *length1, gdouble *length2, gdouble *length3 )
{
g_return_if_fail( element != NULL );
g_return_if_fail( length1 != NULL );
g_return_if_fail( length2 != NULL );
g_return_if_fail( length3 != NULL );
HalfEdge *he = element->adjacent_halfedge;
Point2 *p1 = NODE_POSITION(he->origin);
Point2 *p2 = NODE_POSITION(he->next->origin);
Point2 *p3 = NODE_POSITION(he->next->next->origin);
*length1 = point2_distance( p1, p2 );
*length2 = point2_distance( p2, p3 );
*length3 = point2_distance( p3, p1 );
}
gdouble element_fem_quality( const Element * el )
{
g_return_val_if_fail( el != NULL, G_MAXDOUBLE );
HalfEdge *he = el->adjacent_halfedge;
Point2 *p1 = NODE_POSITION(he->origin);
Point2 *p2 = NODE_POSITION(he->next->origin);
Point2 *p3 = NODE_POSITION(he->previous->origin);
gdouble a, b, c;
a = point2_distance( p1, p2 );
b = point2_distance( p2, p3 );
c = point2_distance( p3, p1 );
// ratio of the longest edge length and the radius of inscribed circle
gdouble h_max = MAX( a, MAX( b, c ) );
gdouble s = ( a + b + c )/2.0;
return 2.0 * SQRT3 * sqrt((s-a)*(s-b)*(s-c)/s) / h_max;
}
void triangle_angles( const Point2 *p1, const Point2 *p2, const Point2 *p3,
gdouble *angle1, gdouble *angle2, gdouble *angle3 )
{
g_return_if_fail( p1 != NULL );
g_return_if_fail( p2 != NULL );
g_return_if_fail( p3 != NULL );
g_return_if_fail( angle1 != NULL );
g_return_if_fail( angle2 != NULL );
g_return_if_fail( angle3 != NULL );
gdouble a, b, c;
a = point2_distance( p2, p3 );
b = point2_distance( p1, p3 );
c = point2_distance( p1, p2 );
gdouble aa = a*a;
gdouble bb = b*b;
gdouble cc = c*c;
*angle1 = acos( (bb+cc-aa)/(2.0*b*c) );
*angle2 = acos( (aa+cc-bb)/(2.0*a*c) );
*angle3 = acos( (aa+bb-cc)/(2.0*a*b) );
}
int test_point2( int argc, char *argv[] )
{
Point2 p1, p2, p3, p;
point2_set( &p1, 1.23456789, 4.678692 );
g_return_val_if_fail( p1.x == 1.23456789, 1 );
g_return_val_if_fail( p1.y == 4.678692, 1 );
point2_set( &p1, -1.0, 0.0 );
point2_set( &p2, 0.0, 1.0 );
g_return_val_if_fail( fabs( point2_distance( &p1, &p2 ) - sqrt(2.0) ) < SMALL_NUMBER, 1 );
point2_set( &p1, 0.0, 1.0 );
point2_set( &p2, -1.0, 0.0 );
point2_set( &p3, 1.0, 0.0 );
point2_set( &p, 0.0, 0.5 );
g_return_val_if_fail( point2_is_in_triangle( &p, &p1, &p2, &p3 ), 1 );
point2_set( &p, 0.0, 0.0 );
g_return_val_if_fail( ! point2_is_in_triangle( &p, &p1, &p2, &p3 ), 1 );
point2_set( &p, 0.5, 0.5 );
g_return_val_if_fail( ! point2_is_in_triangle( &p, &p1, &p2, &p3 ), 1 );
point2_set( &p, 0.5, 0.5 );
g_return_val_if_fail( ! point2_is_in_triangle( &p, &p1, &p2, &p3 ), 1 );
point2_set( &p, 1.0, 0.0 );
g_return_val_if_fail( ! point2_is_in_triangle( &p, &p1, &p2, &p3 ), 1 );
point2_set( &p1, -1.0, -1.0 );
point2_set( &p2, 1.0, 1.0 );
p = point2_interpolate( &p1, &p2, 0.0 );
g_return_val_if_fail( p.x == p1.x, 1 );
g_return_val_if_fail( p.y == p1.y, 1 );
p = point2_interpolate( &p1, &p2, 1.0 );
g_return_val_if_fail( p.x == p2.x, 1 );
g_return_val_if_fail( p.y == p2.y, 1 );
p = point2_interpolate( &p1, &p2, 0.5 );
g_return_val_if_fail( fabs( p.x ) < DBL_EPSILON, 1 );
g_return_val_if_fail( fabs( p.y ) < DBL_EPSILON, 1 );
return 0;
}
polygon2_t* polygon2_star(point2_t* x0, point2_t* points, int num_points)
{
// Make sure x0 is not one of the points.
for (int i = 0; i < num_points; ++i)
{
if (point2_distance(x0, &points[i]) < 1e-14)
polymec_error("polygon2_star: Point %d coincides with x0.", i);
}
// Sort the points by angles.
star_angle_t angles[num_points];
for (int i = 0; i < num_points; ++i)
{
angles[i].angle = atan2(points[i].y - x0->y, points[i].x - x0->x);
angles[i].index = i;
}
qsort(angles, (size_t)num_points, sizeof(star_angle_t), star_angle_cmp);
// Create a polygon from the new ordering.
int ordering[num_points];
for (int i = 0; i < num_points; ++i)
ordering[i] = angles[i].index;
return polygon2_new_with_ordering(points, ordering, num_points);
}
gdouble edge_length( const Edge *edge )
{
Point2 *p1 = NODE_POSITION( edge->he[0].origin );
Point2 *p2 = NODE_POSITION( edge->he[1].origin );
return point2_distance( p1, p2 );
}
