Module math 

Geometric math utilities.

Port of agg_math.h and agg_sqrt_tables.cpp — distances, intersections, cross products, triangle operations, fast integer sqrt, and Bessel functions.

Constants

INTERSECTION_EPSILON

Epsilon for intersection calculations.

VERTEX_DIST_EPSILON

Coinciding points maximal distance (epsilon).

Functions

besj

Bessel function of the first kind of order n.

calc_distance

Euclidean distance between two points.

calc_intersection

Calculate the intersection point of two line segments: (ax,ay)→(bx,by) and (cx,cy)→(dx,dy). Returns Some((x, y)) if they intersect, None if parallel.

calc_line_point_distance

Signed distance from point (x, y) to the infinite line through (x1,y1)→(x2,y2). Positive means left side, negative means right side. If the line segment is degenerate (length < VERTEX_DIST_EPSILON), returns the distance from (x,y) to (x1,y1).

calc_orthogonal

Calculate the orthogonal displacement vector of magnitude thickness perpendicular to the line (x1,y1)→(x2,y2).

calc_polygon_area

Signed area of a polygon defined by a slice of points with x and y fields.

calc_polygon_area_vd

Signed area of a polygon defined by a slice of VertexDist. Same algorithm as calc_polygon_area but works with VertexDist slices (needed by vcgen_contour).

calc_segment_point_sq_distance

Squared distance from point (x, y) to the closest point on segment (x1,y1)→(x2,y2).

calc_segment_point_sq_distance_with_u

Squared distance from point (x, y) to the closest point on segment (x1,y1)→(x2,y2), given pre-computed parameter u.

calc_segment_point_u

Compute the parameter u for the projection of point (x, y) onto the line segment (x1,y1)→(x2,y2). Returns 0 if the segment is degenerate.

calc_sq_distance

Squared Euclidean distance between two points.

calc_triangle_area

Signed area of triangle (x1,y1), (x2,y2), (x3,y3).

cross_product

Cross product of vectors (x2-x1, y2-y1) and (x-x2, y-y2). The sign indicates which side of the line (x1,y1)→(x2,y2) the point (x,y) is on.

dilate_triangle

Dilate a triangle by distance d, producing 6 output points (two per edge). Returns ([x0..x5], [y0..y5]).

fast_sqrt

Fast integer square root using lookup tables. No divisions, multiplications, or loops — just bit shifts and table lookups. Port of C++ fast_sqrt (portable C path).

intersection_exists

Quick check whether two line segments (x1,y1)→(x2,y2) and (x3,y3)→(x4,y4) intersect (boundary excluded).

point_in_triangle

Test if point (x, y) is inside triangle (x1,y1), (x2,y2), (x3,y3).