/**
* Returns the length of a circular arc segment
*/
double
lw_arc_length(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
POINT2D C;
double radius_A, circumference_A;
int a2_side, clockwise;
double a1, a3;
double angle;
if ( lw_arc_is_pt(A1, A2, A3) )
return 0.0;
radius_A = lw_arc_center(A1, A2, A3, &C);
/* Co-linear! Return linear distance! */
if ( radius_A < 0 )
{
double dx = A1->x - A3->x;
double dy = A1->y - A3->y;
return sqrt(dx*dx + dy*dy);
}
/* Closed circle! Return the circumference! */
circumference_A = M_PI * 2 * radius_A;
if ( p2d_same(A1, A3) )
return circumference_A;
/* Determine the orientation of the arc */
a2_side = lw_segment_side(A1, A3, A2);
/* The side of the A1/A3 line that A2 falls on dictates the sweep
direction from A1 to A3. */
if ( a2_side == -1 )
clockwise = LW_TRUE;
else
clockwise = LW_FALSE;
/* Angles of each point that defines the arc section */
a1 = atan2(A1->y - C.y, A1->x - C.x);
a3 = atan2(A3->y - C.y, A3->x - C.x);
/* What's the sweep from A1 to A3? */
if ( clockwise )
{
if ( a1 > a3 )
angle = a1 - a3;
else
angle = 2*M_PI + a1 - a3;
}
else
{
if ( a3 > a1 )
angle = a3 - a1;
else
angle = 2*M_PI + a3 - a1;
}
/* Length as proportion of circumference */
return circumference_A * (angle / (2*M_PI));
}
int
ptarrayarc_contains_point_partial(const POINTARRAY *pa, const POINT2D *pt, int check_closed, int *winding_number)
{
int wn = 0;
int i, side;
const POINT2D *seg1;
const POINT2D *seg2;
const POINT2D *seg3;
GBOX gbox;
/* Check for not an arc ring (always have odd # of points) */
if ( (pa->npoints % 2) == 0 )
{
lwerror("ptarrayarc_contains_point called with even number of points");
return LW_OUTSIDE;
}
/* Check for not an arc ring (always have >= 3 points) */
if ( pa->npoints < 3 )
{
lwerror("ptarrayarc_contains_point called too-short pointarray");
return LW_OUTSIDE;
}
/* Check for unclosed case */
seg1 = getPoint2d_cp(pa, 0);
seg3 = getPoint2d_cp(pa, pa->npoints-1);
if ( check_closed && ! p2d_same(seg1, seg3) )
{
lwerror("ptarrayarc_contains_point called on unclosed ring");
return LW_OUTSIDE;
}
/* OK, it's closed. Is it just one circle? */
else if ( p2d_same(seg1, seg3) && pa->npoints == 3 )
{
double radius, d;
POINT2D c;
seg2 = getPoint2d_cp(pa, 1);
/* Wait, it's just a point, so it can't contain anything */
if ( lw_arc_is_pt(seg1, seg2, seg3) )
return LW_OUTSIDE;
/* See if the point is within the circle radius */
radius = lw_arc_center(seg1, seg2, seg3, &c);
d = distance2d_pt_pt(pt, &c);
if ( FP_EQUALS(d, radius) )
return LW_BOUNDARY; /* Boundary of circle */
else if ( d < radius )
return LW_INSIDE; /* Inside circle */
else
return LW_OUTSIDE; /* Outside circle */
}
else if ( p2d_same(seg1, pt) || p2d_same(seg3, pt) )
{
return LW_BOUNDARY; /* Boundary case */
}
/* Start on the ring */
seg1 = getPoint2d_cp(pa, 0);
for ( i=1; i < pa->npoints; i += 2 )
{
seg2 = getPoint2d_cp(pa, i);
seg3 = getPoint2d_cp(pa, i+1);
/* Catch an easy boundary case */
if( p2d_same(seg3, pt) )
return LW_BOUNDARY;
/* Skip arcs that have no size */
if ( lw_arc_is_pt(seg1, seg2, seg3) )
{
seg1 = seg3;
continue;
}
/* Only test segments in our vertical range */
lw_arc_calculate_gbox_cartesian_2d(seg1, seg2, seg3, &gbox);
if ( pt->y > gbox.ymax || pt->y < gbox.ymin )
{
seg1 = seg3;
continue;
}
/* Outside of horizontal range, and not between end points we also skip */
if ( (pt->x > gbox.xmax || pt->x < gbox.xmin) &&
(pt->y > FP_MAX(seg1->y, seg3->y) || pt->y < FP_MIN(seg1->y, seg3->y)) )
{
seg1 = seg3;
continue;
}
side = lw_arc_side(seg1, seg2, seg3, pt);
/* On the boundary */
if ( (side == 0) && lw_pt_in_arc(pt, seg1, seg2, seg3) )
{
return LW_BOUNDARY;
}
/* Going "up"! Point to left of arc. */
if ( side < 0 && (seg1->y <= pt->y) && (pt->y < seg3->y) )
{
wn++;
}
/* Going "down"! */
if ( side > 0 && (seg2->y <= pt->y) && (pt->y < seg1->y) )
{
wn--;
}
/* Inside the arc! */
if ( pt->x <= gbox.xmax && pt->x >= gbox.xmin )
{
POINT2D C;
double radius = lw_arc_center(seg1, seg2, seg3, &C);
double d = distance2d_pt_pt(pt, &C);
/* On the boundary! */
if ( d == radius )
return LW_BOUNDARY;
/* Within the arc! */
if ( d < radius )
{
/* Left side, increment winding number */
if ( side < 0 )
wn++;
/* Right side, decrement winding number */
if ( side > 0 )
wn--;
}
}
seg1 = seg3;
}
/* Sent out the winding number for calls that are building on this as a primitive */
if ( winding_number )
*winding_number = wn;
/* Outside */
if (wn == 0)
{
return LW_OUTSIDE;
}
/* Inside */
return LW_INSIDE;
}