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Ball-Triangle Collision

Goal: I have a ball in a triangle. The ball has an initial position and velocity. I'm trying to figure out which side of the triangle the ball will hit.

What I've Tried: I derived a formula that outputs which side the ball will hit, by parametrizing the ball's path and the triangle's sides, and finding the minimum time that satisfies the parametric equations. But when I implement this formula into my program, it produces the wrong results! I've tried many things, to no avail. Any help is greatly appreciated. The MWE is here: CodePen

enter image description here

let angle = 0;
let sides = [];
let vertices = [];

const len = 100;

function setup() {
  createCanvas(windowWidth, windowHeight);
  angleMode(DEGREES);

  angleOne = createSlider(0, 89, 60);
  angleOne.position(10, 10);
  angleOne.style("width", "80px");

  angleTwo = createSlider(0, 89, 60);
  angleTwo.position(10, 30);
  angleTwo.style("width", "80px");

  // Initial vertice & side setup (these don't change)
  let v1 = createVector(width / 2 - len / 2, height * 0.7);
  let v2 = createVector(width / 2 + len / 2, height * 0.7);

  sides[0] = new Side(v1.x, v1.y, v2.x, v2.y, "green");

  vertices[0] = new Vertex(v1.x, v1.y);
  vertices[1] = new Vertex(v2.x, v2.y);
}

function draw() {
  background(255);

  let angOne = angleOne.value();
  let angTwo = angleTwo.value();
  fill(0);
  strokeWeight(0);
  textSize(15);
  text(angOne, 100, 25);
  text(angTwo, 100, 45);

  let v2Offset = createVector(len * cos(-angOne), len * sin(-angOne));
  let v3Offset = createVector(-len * cos(angTwo), -len * sin(angTwo));

  vertices[2] = new Vertex(
    vertices[0].a.x + v2Offset.x,
    vertices[0].a.y + v2Offset.y
  );
  vertices[3] = new Vertex(
    vertices[1].a.x + v3Offset.x,
    vertices[1].a.y + v3Offset.y
  );

  // Update the sides
  sides[1] = new Side(
    vertices[0].a.x,
    vertices[0].a.y,
    vertices[2].a.x,
    vertices[2].a.y
  );

  sides[3] = new Side(
    vertices[1].a.x,
    vertices[1].a.y,
    vertices[3].a.x,
    vertices[3].a.y
  );

  const m1 =
    (vertices[2].a.y - vertices[0].a.y) / (vertices[2].a.x - vertices[0].a.x);

  const m2 =
    (vertices[3].a.y - vertices[1].a.y) / (vertices[3].a.x - vertices[1].a.x);

  // Calculate the y-offset relative to vertices[0]
  const b2 = (vertices[1].a.x - vertices[0].a.x) * -m2;

  const xInt = b2 / (m1 - m2);
  const yInt = xInt * m1;
  // Note xInt and yInt are relative to vertices[0]

  // draw all the things
  // sides.forEach((s) => s.show());

  // stroke(0, 255, 0);
  // strokeWeight(20);
  point(vertices[0].a.x + xInt, vertices[0].a.y + yInt);

  vertices[4] = new Vertex(vertices[0].a.x + xInt, vertices[0].a.y + yInt);

  sides[4] = new Side(
    vertices[1].a.x,
    vertices[1].a.y,
    vertices[0].a.x + xInt,
    vertices[0].a.y + yInt,
    "blue"
  );

  sides[5] = new Side(
    vertices[0].a.x,
    vertices[0].a.y,
    vertices[0].a.x + xInt,
    vertices[0].a.y + yInt,
    "purple"
  );

  scale(2); // so I can make the triangle actually *visible*
  translate(-width / 3, -height / 4);

  sides[0].show();
  sides[4].show();
  sides[5].show();

  vertices[0].show();
  vertices[1].show();
  vertices[4].show();

  strokeWeight(1);
  stroke(255, 0, 0);
  noFill();
  arc(vertices[0].a.x, vertices[0].a.y, 40, 40, -1 * angleOne.value(), 0, PIE);
  arc(
    vertices[1].a.x,
    vertices[1].a.y,
    40,
    40, -180, -(180 - angleTwo.value()),
    PIE
  );

  let P1x = vertices[0].a.x;
  let P1y = vertices[0].a.y;

  let P2x = vertices[1].a.x;
  let P2y = vertices[1].a.y;

  let P3x = vertices[4].a.x;
  let P3y = vertices[4].a.y;

  stroke(255, 255, 0);
  stroke("purple"); // Change the color
  strokeWeight(5); // Make the points 10 pixels in size

  let P0 = createVector(P1x + 60, P1y - 40);
  let V0 = createVector(0, -15);

  point(P0.x, P0.y);
  stroke(255, 0, 0);
  point(P0.x + V0.x, P0.y + V0.y);
  strokeWeight(2);
  stroke("purple");
  line(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);

  // console.log(P1x,P1y,P2x,P2y,P3x,P3y);

  let A1 = P3y - P1y;
  let B1 = -(P3x - P1x);
  let C1 = A1 * P1x + B1 * P1y;

  let A2 = -(P3y - P2y);
  let B2 = P3x - P2x;
  let C2 = A2 * P2x + B2 * P2y;

  let A3 = -(P2y - P1y);
  let B3 = P2x - P1x;
  let C3 = A3 * P2x + B3 * P2y;

  let t1 = (C1 - A1 * P0.x - B1 * P0.y) / (A1 * V0.x + B1 * P0.y);
  let t2 = (C2 - A2 * P0.x - B2 * P0.y) / (A2 * V0.x + B2 * P0.y);
  let t3 = (C3 - A3 * P0.x - B3 * P0.y) / (A3 * V0.x + B3 * P0.y);

  let times = [t1, t2, t3];
  let posTimes = [];

  for (let i = 0; i < times.length; i++) {
    times[i] = round(times[i], 2);
  }

  // console.log("After rounding:", times);

  for (let i = 0; i < times.length; i++) {
    if (times[i] > 0) {
      posTimes.push(times[i]);
    }
  }

  // console.log("posTimes:", posTimes);
  trueTime = min(posTimes);
  if (trueTime == round(t1, 2)) {
    fill("Blue");
    text("Hit Blue", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
  } else if (trueTime == round(t2, 2)) {
    fill("Green");
    text("Hit Green", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
  } else {
    fill("Purple");
    text("Hit Purple", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
  }
}

class Side {
  constructor(x1, y1, x2, y2, col = "black") {
    this.a = createVector(x1, y1);
    this.b = createVector(x2, y2);
    this.color = col;
  }

  show() {
    stroke(this.color);
    strokeWeight(4);
    line(this.a.x, this.a.y, this.b.x, this.b.y);
  }
}

class Vertex {
  constructor(x1, y1) {
    this.a = createVector(x1, y1);
  }

  show() {
    stroke(255, 0, 0);
    strokeWeight(10);
    point(this.a.x, this.a.y);
  }
}
html, body { margin: 0; padding: 0; overflow: hidden }
<script src="https://cdn.jsdelivr.net/npm/p5@1.4.1/lib/p5.min.js"></script>

over 4 years ago · Santiago Trujillo
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