Line and segment intersection

packages/math/line.ts

@@ -1,5 +1,6 @@
-import { pointCenter, pointRotateRads } from "./point";
-import type { GenericPoint, Line, Radians } from "./types";
+import { point, pointCenter, pointRotateRads } from "./point";
+import { segmentIncludesPoint } from "./segment";
+import type { GenericPoint, Line, Radians, Segment } from "./types";
 
 /**
  * Create a line from two points.
@@ -40,13 +41,55 @@ export function lineFromPointArray<P extends GenericPoint>(
 
 // return the coordinates resulting from rotating the given line about an origin by an angle in degrees
 // note that when the origin is not given, the midpoint of the given line is used as the origin
-export const lineRotate = <Point extends GenericPoint>(
+export function lineRotate<Point extends GenericPoint>(
   l: Line<Point>,
   angle: Radians,
   origin?: Point,
-): Line<Point> => {
+): Line<Point> {
   return line(
     pointRotateRads(l[0], origin || pointCenter(l[0], l[1]), angle),
     pointRotateRads(l[1], origin || pointCenter(l[0], l[1]), angle),
   );
-};
+}
+
+/**
+ * Returns the intersection point of two infinite lines, if any
+ *
+ * @param a One of the line to intersect
+ * @param b Another line to intersect
+ * @returns The intersection point
+ */
+export function lineIntersectsLine<Point extends GenericPoint>(
+  [[x1, y1], [x2, y2]]: Line<Point>,
+  [[x3, y3], [x4, y4]]: Line<Point>,
+): Point | null {
+  const a = x1 * y2 - x2 * y1;
+  const c = x3 * y4 - x4 * y3;
+  const den = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
+  if (den === 0) {
+    return null;
+  }
+  const xnum = a * (x3 - x4) - (x1 - x2) * c;
+  const ynum = a * (y3 - y4) - (y1 - y2) * c;
+
+  return point<Point>(xnum / den, ynum / den);
+}
+
+/**
+ * Returns the intersection point of a segment and a line
+ *
+ * @param l
+ * @param s
+ * @returns
+ */
+export function lineIntersectsSegment<Point extends GenericPoint>(
+  l: Line<Point>,
+  s: Segment<Point>,
+): Point | null {
+  const candidate = lineIntersectsLine(l, line(s[0], s[1]));
+  if (!candidate || !segmentIncludesPoint(candidate, s)) {
+    return null;
+  }
+
+  return candidate;
+}