doodler/collision/sat.ts

import { Polygon } from "../geometry/polygon.ts";
import { SplineSegment } from "../geometry/spline.ts";
import { Vector } from "../geometry/vector.ts";
import { axisAlignedBoundingBox } from "./aa.ts";
import { CircleLike } from "./circular.ts";

export function satCollisionSpline(p: Polygon, spline: SplineSegment): boolean {
  const numSegments = 100; // You can adjust the number of segments based on your needs

  for (let i = 0; i < numSegments; i++) {
    const t1 = i / numSegments;
    const t2 = (i + 1) / numSegments;

    const segmentStart = spline.getPointAtT(t1);
    const segmentEnd = spline.getPointAtT(t2);

    if (segmentIntersectsPolygon(p, segmentStart, segmentEnd)) {
      return true;
    }
  }

  return false;
}

export function satCollisionPolygon(poly: Polygon, poly2: Polygon): boolean {
  for (const edge of poly.getEdges()) {
    const axis = edge.copy().normal().normalize();
    const proj1 = projectPolygonOntoAxis(poly, axis);
    const proj2 = projectPolygonOntoAxis(poly2, axis);

    if (!overlap(proj1, proj2)) return false;
  }
  for (const edge of poly2.getEdges()) {
    const axis = edge.copy().normal().normalize();
    const proj1 = projectPolygonOntoAxis(poly, axis);
    const proj2 = projectPolygonOntoAxis(poly2, axis);

    if (!overlap(proj1, proj2)) return false;
  }
  return true;
}
export function satCollisionCircle(p: Polygon, circle: CircleLike): boolean {
  for (const edge of p.getEdges()) {
    const axis = edge.copy().normal().normalize();
    const proj1 = projectPolygonOntoAxis(p, axis);
    const proj2 = projectCircleOntoAxis(circle, axis);

    if (!overlap(proj1, proj2)) return false;
  }
  const center = new Vector(circle.center);
  const nearest = p.getNearestPoint(center);
  const axis = nearest.copy().sub(center).normalize();
  const proj1 = projectPolygonOntoAxis(p, axis);
  const proj2 = projectCircleOntoAxis(circle, axis);

  if (!overlap(proj1, proj2)) return false;
  return true;
}
export function satCollisionAABBCircle(
  aabb: axisAlignedBoundingBox,
  circle: CircleLike,
): boolean {
  const p = new Polygon([
    { x: aabb.x, y: aabb.y },
    { x: aabb.x + aabb.w, y: aabb.y },
    { x: aabb.x + aabb.w, y: aabb.y + aabb.h },
    { x: aabb.x, y: aabb.y + aabb.h },
  ]);
  return satCollisionCircle(p, circle);
}

function segmentIntersectsPolygon(
  p: Polygon,
  start: Vector,
  end: Vector,
): boolean {
  const edges = p.getEdges();

  for (const edge of edges) {
    // const axis = new Vector(-edge.y, edge.x).normalize();
    const axis = edge.copy().normal().normalize();

    const proj1 = projectPolygonOntoAxis(p, axis);
    const proj2 = projectSegmentOntoAxis(start, end, axis);

    if (!overlap(proj1, proj2)) {
      return false; // No overlap, no intersection
    }
  }

  return true; // Overlapping on all axes, intersection detected
}

function projectPolygonOntoAxis(
  p: Polygon,
  axis: Vector,
): { min: number; max: number } {
  let min = Infinity;
  let max = -Infinity;

  for (const point of p.points) {
    const dotProduct = point.copy().add(p.center).dot(axis);
    min = Math.min(min, dotProduct);
    max = Math.max(max, dotProduct);
  }

  return { min, max };
}

function projectSegmentOntoAxis(
  start: Vector,
  end: Vector,
  axis: Vector,
): { min: number; max: number } {
  const dotProductStart = start.dot(axis);
  const dotProductEnd = end.dot(axis);
  return {
    min: Math.min(dotProductStart, dotProductEnd),
    max: Math.max(dotProductStart, dotProductEnd),
  };
}

function projectCircleOntoAxis(
  c: CircleLike,
  axis: Vector,
): { min: number; max: number } {
  const dot = new Vector(c.center).dot(axis);
  const min = dot - c.radius;
  const max = dot + c.radius;
  return { min, max };
}

function overlap(
  proj1: { min: number; max: number },
  proj2: { min: number; max: number },
): boolean {
  return proj1.min <= proj2.max && proj1.max >= proj2.min;
}