void DaoxCanvas_Rotate( int x, int y )
{
DaoxMatrix3D rotate = {1.0,0.0,0.0,0.0,1.0,0.0};
DaoxAABBox2D box = daox_current_canvas->viewport;
DaoxVector2D start, end, center = {0.0,0.0};
double W2 = 0.5 * window_width;
double H2 = 0.5 * window_height;
double area, cosine, sine;
start.x = last_x - W2;
start.y = last_y - H2;
end.x = x - W2;
end.y = y - H2;
area = DaoxTriangle_Area( center, start, end );
cosine = DaoxTriangle_AngleCosine( center, start, end );
sine = sqrt( 1.0 - cosine * cosine );
rotate.A11 = rotate.A22 = cosine;
if( area < 0.0 ){
rotate.A12 = - sine;
rotate.A21 = sine;
}else{
rotate.A12 = sine;
rotate.A21 = - sine;
}
DaoxMatrix3D_Multiply( & daox_current_canvas->transform, rotate );
Done:
last_x = x;
last_y = y;
}
void DaoxWindow_RotateCanvas( DaoxWindow *self, DaoxCanvas *canvas, int x, int y )
{
DaoxMatrix3D rotate = {1.0,0.0,0.0,0.0,1.0,0.0};
DaoxVector2D start, end, center = {0.0,0.0};
double W2 = 0.5 * self->width;
double H2 = 0.5 * self->height;
double area, cosine, sine;
start.x = self->cursorPosX - W2;
start.y = self->cursorPosY - H2;
end.x = x - W2;
end.y = y - H2;
area = DaoxTriangle_Area( center, start, end );
cosine = DaoxTriangle_AngleCosine( center, start, end );
sine = sqrt( 1.0 - cosine * cosine );
rotate.A11 = rotate.A22 = cosine;
if( area < 0.0 ){
rotate.A12 = - sine;
rotate.A21 = sine;
}else{
rotate.A12 = sine;
rotate.A21 = - sine;
}
DaoxMatrix3D_Multiply( & canvas->transform, rotate );
}
void DaoxTriangulator_InitContourOrientation( DaoxTriangulator *self )
{
DaoxVertexData *vertex, *start, *vmax = NULL;
DaoxVector2D A, B, C, *points = self->points->data.vectors2d;
int i, dir, N = self->vertices->size;
float xmax, ymax;
/* sort vertices by the x coordinates: */
DaoxTriangulator_SortVertices( self );
for(i=0; i<N; ++i){
start = self->vertices->items.pVoid[i];
if( start->direction != 0 ) continue;
A = points[start->index];
xmax = A.x;
ymax = A.y;
vertex = vmax = start;
do {
A = points[vertex->index];
if( A.x >= xmax ){
if( A.x > xmax || A.y > ymax ){
xmax = A.x;
ymax = A.y;
vmax = vertex;
}
}
vertex = vertex->next;
} while( vertex != start );
A = points[vmax->index];
B = points[vmax->next->index];
C = points[vmax->prev->index];
dir = DaoxTriangle_Area( A, B, C ) > 0.0 ? DAOX_COUNTER_CW : DAOX_CLOCKWISE;
//printf( "contour = %i dir = %i\n", (int)vmax->contour, dir );
vertex = start;
do {
vertex->direction = dir;
vertex = vertex->next;
} while( vertex != start );
}
}
void DaoxTriangulator_Triangulate( DaoxTriangulator *self )
{
DaoxVertexData *V, *A, *B, *C, *inside;
DaoxVector2D PA, PB, PC, P, *points = self->points->data.vectors2d;
int i, imin, imax, contours, K = 0, N = self->vertices->size;
double dist, area, ymin, ymax, dmax, dmin;
double AB, BC, CA, min_area = 1E-16;
if( self->vertices->size == 0 ) return;
DaoxTriangulator_InitContourOrientation( self );
V = (DaoxVertexData*) self->vertices->items.pVoid[N-1];
contours = V->contour;
DList_Assign( self->worklist, self->vertices );
while( self->worklist->size && (++K) < 10*N ){
A = (DaoxVertexData*) self->worklist->items.pVoid[self->worklist->size-1];
if( A->done ){
DList_PopBack( self->worklist );
continue;
}
B = A->next;
C = A->prev;
PA = points[A->index];
PB = points[B->index];
PC = points[C->index];
area = DaoxTriangle_Area( PA, PB, PC );
if( B->next == C ){ /* already a triangle: */
if( fabs( area ) > min_area ) DaoxTriangulator_MakeTriangle( self, A );
A->next->prev = A->prev;
A->prev->next = A->next;
A->done = B->done = C->done = 1;
DList_PopBack( self->worklist );
continue;
}
ymin = ymax = PA.y;
if( PB.y < ymin ) ymin = PB.y; else if( PB.y > ymax ) ymax = PB.y;
if( PC.y < ymin ) ymin = PC.y; else if( PC.y > ymax ) ymax = PC.y;
imin = B->sorting < C->sorting ? B->sorting : C->sorting;
imax = A->sorting;
inside = NULL;
dmax = - 1.0;
dmin = 1E9;
/*
// find the closest point to the triangle:
//
// Note: no need to distinguish duplicated vertices, because:
// 1. if they are outside of the trianlge, they cause no problem;
// 2. they cannot be the "closest" vertex to "A" or another vertex again,
// so no problem for joining inner contour or splitting outer contour.
//
// The reason that they cannot be the "closest" vertex is that,
// only a concave vertex from the outer contour or a convex
// vertex from an inner contour for a hole can be chosen as the
// the "closest" vertex.
//
// And when its original vertex was choose as the "closest" vertex,
// the associated "A" will always be processed until it is removed
// from the polygon(s), which will leave the duplicated vertices
// as convex vertices on the outer contour!
*/
for(i=imin+1; i<imax; ++i){
V = (DaoxVertexData*) self->vertices->items.pVoid[i];
P = points[V->index];
if( V->done ) continue;
//printf( "%3i: %12f %12f %9p, %3i %3i %3i %3i\n", i, P.x, P.y, V, V->contour, A->contour, V->direction, A->direction );
/* Ingore vertex from other contour with the same direction: */
if( V->contour != A->contour && V->direction == A->direction ) continue;
if( V->sorting == A->sorting || V->sorting == B->sorting || V->sorting == C->sorting )
continue;
if( P.y > ymax ) continue;
if( P.y < ymin ) continue;
//printf( "%3i: %12f %12f %9p, %3i %3i %3i %3i\n", i, P.x, P.y, V, V->contour, A->contour, V->direction, A->direction );
BC = DaoxTriangle_Area( P, PB, PC );
AB = DaoxTriangle_Area( P, PA, PB );
CA = DaoxTriangle_Area( P, PC, PA );
if( area < 0.0 ){
AB = -AB;
BC = -BC;
CA = -CA;
}
//printf( "%3i: %12f %12f %12f\n", i, AB, BC, CA );
if( BC >= 0.0 && AB >= 0.0 && CA >= 0.0 ){
float d = DaoxVector2D_Dist( P, PA );
if( d < dmin ){
dmin = d;
inside = V;
}
}
}
#if 0
printf( "A: %15f %15f %9p\n", PA.x, PA.y, A );
printf( "B: %15f %15f %9p\n", PB.x, PB.y, B );
printf( "C: %15f %15f %9p\n", PC.x, PC.y, C );
if( inside ) printf( "I: %15f %15f\n", points[inside->index].x, points[inside->index].y );
printf( "%p\n", inside );
printf( "area: %15f\n", area );
#endif
if( inside == NULL ){
A->done = 1;
//printf( "area: %15f\n", DaoxTriangle_Area( PA, PB, PC ) );
if( fabs( area ) > min_area ) DaoxTriangulator_MakeTriangle( self, A );
A->next->prev = A->prev;
A->prev->next = A->next;
DList_PopBack( self->worklist );
//if( self->triangles->size >= 3*111 ) break;
}else{ /* point inside the triangle: */
DaoxVertexData *A2, *N2;
int breaking = inside->contour == A->contour;
if( inside->contour != A->contour ){ /* joining contour: */
/* the "inside" vertex is from a hole: */
DaoxVertexData *V2 = inside;
//printf( "joining\n" );
/* update contour: */
do {
V2->contour = A->contour;
V2->direction = A->direction;
V2 = V2->next;
} while( V2 != inside );
}
/*
// connect "inside" to "A" with duplicated vertices, this will either:
// 1. connect the inner contour with the outer contour;
// 2. or break the outer contour.
*/
N2 = DaoxTriangulator_GetVertex( self, inside->index );
A2 = DaoxTriangulator_GetVertex( self, A->index );
N2->sorting = inside->sorting;
A2->sorting = A->sorting;
A2->contour = N2->contour = A->contour;
A2->direction = N2->direction = A->direction;
A2->prev = A->prev; A->prev->next = A2;
A2->next = N2; N2->prev = A2;
N2->next = inside->next; inside->next->prev = N2;
inside->next = A; A->prev = inside;
//printf( "dup: %9p %9p\n", A2, N2 );
if( breaking ){
contours += 1;
//printf( "contours = %3i\n", contours );
DaoxVertexData *V2 = inside;
/* update contour: */
do {
V2->contour = contours;
V2 = V2->next;
} while( V2 != inside );
}
DList_PushBack( self->vertices, N2 );
DList_PushBack( self->vertices, A2 );
DList_PopBack( self->worklist );
DList_PushBack( self->worklist, N2 );
DList_PushBack( self->worklist, A2 );
DList_PushBack( self->worklist, A );
}
}
}