circle_raycast_intersections()

static int circle_raycast_intersections ( const POINT2D *  center, double  radius, double  ray, POINT2D *  i0, POINT2D *  i1  )

static

Calculates the intersection points of a circle and a horizontal line.

The equation of a circle is (x - cx)^2 + (y - cy)^2 = r^2. The equation of the horizontal line is y = y_line. Substituting y_line into the circle equation gives: (x - cx)^2 = r^2 - (y_line - cy)^2 This function solves for x.

Parameters

center	A pointer to the center point of the circle.
radius	The radius of the circle.
ray	The y-coordinate of the horizontal line.
i0	A pointer to a POINT2D to store the first intersection point.
i1	A pointer to a POINT2D to store the second intersection point.

Returns

The number of intersection points found (0, 1, or 2).

Definition at line 903 of file ptarray.c.

{
        // Calculate the vertical distance from the circle's center to the horizontal line.
        double dy = ray - center->y;
 
        // If the absolute vertical distance is greater than the radius, there are no intersections.
        if (fabs(dy) > radius)
                return 0;
 
        // Use the Pythagorean theorem to find the horizontal distance (dx) from the
        // center's x-coordinate to the intersection points.
        // dx^2 + dy^2 = radius^2  =>  dx^2 = radius^2 - dy^2
        double dx_squared = radius * radius - dy * dy;
 
        // Case 1: One intersection (tangent)
        // This occurs when the line just touches the top or bottom of the circle.
        // dx_squared will be zero. We check against a small epsilon for floating-point safety.
        if (FP_EQUALS(dx_squared, 0.0))
        {
                i0->x = center->x;
                i0->y = ray;
                return 1;
        }
 
        // Case 2: Two intersections
        // The line cuts through the circle.
        double dx = sqrt(dx_squared);
 
        // The first intersection point has the smaller x-value.
        i0->x = center->x - dx;
        i0->y = ray;
 
        // The second intersection point has the larger x-value.
        i1->x = center->x + dx;
        i1->y = ray;
 
        return 2;
}

References FP_EQUALS, POINT2D::x, and POINT2D::y.

Referenced by ptarrayarc_raycast_intersections().

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