球三角碰撞
Ball-Triangle Collision
目标： 我有一个三角球。球具有初始位置和速度。我想弄清楚球会击中三角形的哪一侧。
我试过的： 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
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>
我无法理解你的数学。我认为您应该尝试使用解释性注释来注释此类代码。这通常会帮助您发现自己的错误：
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);
这是一些工作数学。可能不是最多的dense/elegant，但是我试着从基本的代数开始一步步讲解：
// Find which of
//
// P1 to P2 = green
// P1 to P3 = purple
// P2 to P3 = blue
//
// PO to PO + V0 intersects with
// Find the intersection point between lines A and B
function intersection(Ax1, Ay1, Ax2, Ay2, Bx1, By1, Bx2, By2) {
// Calculate the slope of line A
let Am = (Ay2 - Ay1) / (Ax2 - Ax1);
// Calculate the y-intercept of line A
let Ab = Ay1 - Ax1 * Am;
// slope of line B
let Bm = (By2 - By1) / (Bx2 - Bx1);
// y-intercept of line B
let Bb = By1 - Bx1 * Bm;
if (Am === Bm) {
// Parallel lines
return;
}
if (!Number.isFinite(Am)) {
// Line A is vertical
if (!Number.isFinite(Bm)) {
// Line B is also vertical (Am may not equal Bm though because Infinity != NegativeInfinity)
return;
} else {
// Since line A is vertical, intersection point will lie along the same x position as Ax1 and Ax2
const xInt = Ax1;
// Simply use the equation for line segment B to find the corresponding Y value
const yInt = Bm * xInt + Bb;
return createVector(xInt, yInt);
}
} else if (!Number.isFinite(Bm)) {
// Line B is vertical
const xInt = Bx1;
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
} else {
// Derived from Am * x + Ab = Bm * x + Bb
const xInt = (Bb - Ab) / (Am - Bm);
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
}
}
let P1toP2int =
intersection(P1.x, P1.y, P2.x, P2.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P1toP3int =
intersection(P1.x, P1.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P2toP3int =
intersection(P2.x, P2.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
// These intersection points assume that all lines point infinitely in both
// directions, so we still have some more work to do.
// Check if each of these points is within the target segment
function isWithin(lineX1, lineY1, lineX2, lineY2, xInt, yInt) {
if (abs((lineY2 - lineY1) / (lineX2 - lineX1)) > 1) {
// If the line segment is more vertical, check the Y position
return yInt >= min(lineY1, lineY2) && yInt <= max(lineY1, lineY2);
} else {
return xInt >= min(lineX1, lineX2) && xInt <= max(lineX1, lineX2);
}
}
if (P1toP2int && !isWithin(P1.x, P1.y, P2.x, P2.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isWithin(P1.x, P1.y, P3.x, P3.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isWithin(P2.x, P2.y, P3.x, P3.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
// Check if each intersection point is in the direction our ray is pointing
function isOnRay(rayX0, rayY0, rayX1, rayY1, xInt, yInt) {
// If the ray is more vertical, check the y coordinates
if (abs((rayY1 - rayY0) / (rayX1 - rayX0)) > 1) {
// If the ray is pointing in the positive Y direction
// (rayY1 > rayY0) then the yInt must be on the positive
// side of rayY0; and vice versa
return (rayY1 > rayY0) === (yInt > rayY0);
} else {
return (rayX1 > rayX0) === (xInt > rayX0);
}
}
if (P1toP2int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
let angle = 0;
let sides = [];
let vertices = [];
const len = 100;
let angleOne;
let angleTwo;
let angleThree;
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");
angleThree = createSlider(0, 360, 0);
angleThree.position(10, 50);
angleThree.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();
let rayAngle = angleThree.value();
fill(0);
strokeWeight(0);
textSize(15);
text(angOne, 100, 25);
text(angTwo, 100, 45);
text(rayAngle, 100, 65);
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[4].a.x,
vertices[4].a.y,
"blue"
);
sides[5] = new Side(
vertices[0].a.x,
vertices[0].a.y,
vertices[4].a.x,
vertices[4].a.y,
"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 P1 = vertices[0].a;
let P2 = vertices[1].a;
let P3 = vertices[4].a;
stroke(255, 255, 0);
stroke("purple"); // Change the color
strokeWeight(5); // Make the points 10 pixels in size
let P0 = createVector(P1.x + 60, P1.y - 40);
let V0 = createVector(15 * cos(rayAngle), 15 * sin(rayAngle));
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);
// Find which of
//
// P1 to P2 = green
// P1 to P3 = purple
// P2 to P3 = blue
//
// PO to PO + V0 intersects with
// Find the intersection point between lines A and B
function intersection(Ax1, Ay1, Ax2, Ay2, Bx1, By1, Bx2, By2) {
// Calculate the slope of line A
let Am = (Ay2 - Ay1) / (Ax2 - Ax1);
// Calculate the y-intercept of line A
let Ab = Ay1 - Ax1 * Am;
// slope of line B
let Bm = (By2 - By1) / (Bx2 - Bx1);
// y-intercept of line B
let Bb = By1 - Bx1 * Bm;
if (Am === Bm) {
// Parallel lines
return;
}
if (!Number.isFinite(Am)) {
// Line A is vertical
if (!Number.isFinite(Bm)) {
// Line B is also vertical (Am may not equal Bm though because Infinity != NegativeInfinity)
return;
} else {
// Since line A is vertical, intersection point will lie along the same x position as Ax1 and Ax2
const xInt = Ax1;
// Simply use the equation for line segment B to find the corresponding Y value
const yInt = Bm * xInt + Bb;
return createVector(xInt, yInt);
}
} else if (!Number.isFinite(Bm)) {
// Line B is vertical
const xInt = Bx1;
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
} else {
// Derived from Am * x + Ab = Bm * x + Bb
const xInt = (Bb - Ab) / (Am - Bm);
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
}
}
let P1toP2int =
intersection(P1.x, P1.y, P2.x, P2.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P1toP3int =
intersection(P1.x, P1.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P2toP3int =
intersection(P2.x, P2.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
// These intersection points assume that all lines point infinitely in both
// directions, so we still have some more work to do.
// Check if each of these points is within the target segment
function isWithin(lineX1, lineY1, lineX2, lineY2, xInt, yInt) {
if (abs((lineY2 - lineY1) / (lineX2 - lineX1)) > 1) {
// If the line segment is more vertical, check the Y position
return yInt >= min(lineY1, lineY2) && yInt <= max(lineY1, lineY2);
} else {
return xInt >= min(lineX1, lineX2) && xInt <= max(lineX1, lineX2);
}
}
if (P1toP2int && !isWithin(P1.x, P1.y, P2.x, P2.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isWithin(P1.x, P1.y, P3.x, P3.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isWithin(P2.x, P2.y, P3.x, P3.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
// Check if each intersection point is in the direction our ray is pointing
function isOnRay(rayX0, rayY0, rayX1, rayY1, xInt, yInt) {
// If the ray is more vertical, check the y coordinates
if (abs((rayY1 - rayY0) / (rayX1 - rayX0)) > 1) {
// If the ray is pointing in the positive Y direction
// (rayY1 > rayY0) then the yInt must be on the positive
// side of rayY0; and vice versa
return (rayY1 > rayY0) === (yInt > rayY0);
} else {
return (rayX1 > rayX0) === (xInt > rayX0);
}
}
if (P1toP2int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
// Only one of these should be true, except perhaps if the ray passes precisely through a corner
if (P1toP2int) {
stroke("Red");
strokeWeight(8);
point(P1toP2int.x, P1toP2int.y);
fill("Green");
noStroke();
text("Hit Green", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
}
if (P1toP3int) {
stroke("Red");
strokeWeight(8);
point(P1toP3int.x, P1toP3int.y);
fill("Purple");
noStroke();
text("Hit Purple", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
}
if (P2toP3int) {
stroke("Red");
strokeWeight(8);
point(P2toP3int.x, P2toP3int.y);
fill("Blue");
noStroke();
text("Hit Blue", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
}
/* I don't understand this math at all
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>
一条射线(R1, R2)和一条线(L1, L2)的交点可以用Dot Product计算：
N = (L1.y - L2.y, L2.x - L1.x)
t = dot(R1-L1, N) / dot(L2-L1, N)
X = R1 + (R2-R1) * t (if 0 <= t <= 1 and dot(R2-R1, X-R1) > 0)
在p5.js中可以使用p5.Vector:
实现
function intersect_ray_line_segment(r1, r2, l1, l2) {
let R = p5.Vector.sub(r2, r1);
let L = p5.Vector.sub(l2, l1);
let N = p.createVector(-R.y, R.x);
if (L.dot(N) == 0) {
return undefined; // parallel
}
let t = p5.Vector.sub(r1, l1).dot(N) / L.dot(N);
if (t < 0 || t > 1) {
return undefined; // intersection is not on line segment
}
let X = L.mult(t).add(l1);
if (R.dot(p5.Vector.sub(X, r1)) < 0) {
return undefined; // wrong direction
}
return X;
}
示例：
var sketch = function( p ) {
p.setup = function() {
let sketchCanvas = p.createCanvas(p.windowWidth, p.windowHeight);
}
p.windowResized = function() {
p.resizeCanvas(p.windowWidth, p.windowHeight);
}
function intersect_ray_line_segment(r1, r2, l1, l2) {
let R = p5.Vector.sub(r2, r1);
let L = p5.Vector.sub(l2, l1);
let N = p.createVector(-R.y, R.x);
if (L.dot(N) == 0) {
return undefined; // parallel
}
let t = p5.Vector.sub(r1, l1).dot(N) / L.dot(N);
if (t < 0 || t > 1) {
return undefined; // intersection is not on line segment
}
let X = L.mult(t).add(l1);
if (R.dot(p5.Vector.sub(X, r1)) < 0) {
return undefined; // wrong direction
}
return X;
}
function closest_hit_point(r1, r2, points, lines) {
let hit_p = undefined;
let dist = undefined;
let N = undefined;
for (let i = 0; i < lines.length; ++i) {
let l1 = points[lines[i][0]];
let l2 = points[lines[i][1]];
let new_hit_p = intersect_ray_line_segment(r1, r2, points[lines[i][0]], points[lines[i][1]]);
if (new_hit_p) {
let new_d = p5.Vector.dist(r1, new_hit_p);
if (new_d > 0.1 && (!dist || new_d < dist)) {
dist = new_d;
hit_p = new_hit_p;
N = p.createVector(l1.y - l2.y, l2.x - l1.x);
}
}
}
return hit_p ? [hit_p, N] : undefined;
}
p.draw = function() {
let sx = p.width / 2;
let sy = p.height / 2;
let points = [
p.createVector(-sx*0.7, -sy*0.2), p.createVector(-sx*0.7, +sy*0.2),
p.createVector(-sx*0.3, -sy*0.5), p.createVector(sx*0.4, -sy*0.5),
p.createVector(sx*0.6, -sy*0.3), p.createVector(sx*0.6, sy*0.5), p.createVector(-sx*0.3, sy*0.5)];
let lines = [[0, 1], [2, 3], [3, 4], [4, 5], [5, 6]]
let center = new p5.Vector(0, 0);
let mouse_p = p.createVector(p.mouseX - sx, p.mouseY - sy);
let direction = p.createVector(mouse_p.x - center.x, mouse_p.y - center.y);
let hit_points = [center]
if (center.x != mouse_p.x || center.y != mouse_p.y) {
let start = center;
result = closest_hit_point(center, mouse_p, points, lines);
let count = 0
while (result && count < 100) {
hit_points.push(result[0]);
direction = direction.reflect(result[1]);
result = closest_hit_point(result[0], p5.Vector.add(result[0], direction), points, lines);
count ++;
}
}
direction.normalize();
hit_points.push(direction.mult( new p5.Vector(p.width, p.height).mag()).add(hit_points[hit_points.length-1]));
p.translate(p.width/2, p.height/2);
p.background(192);
p.strokeWeight(3);
p.stroke(64, 64, 255);
p.fill(128, 128, 255);
for (let i = 0; i < lines.length; ++i) {
let p0 = points[lines[i][0]];
let p1 = points[lines[i][1]];
p.line(p0.x, p0.y, p1.x, p1.y);
}
for (let i = 0; i < points.length; ++i) {
p.ellipse(points[i].x, points[i].y, 10, 10);
}
p.stroke(0, 0, 0);
p.fill(128, 128, 128);
p.ellipse(center.x, center.y, 10, 10);
for (let i = 1; i < hit_points.length; ++i) {
p.line(hit_points[i-1].x, hit_points[i-1].y, hit_points[i].x, hit_points[i].y);
}
for (let i = 0; i < hit_points.length; ++i) {
p.ellipse(hit_points[i].x, hit_points[i].y, 10, 10);
}
}
};
var circle_3_pts = new p5(sketch);
<script src="https://cdn.jsdelivr.net/npm/p5@1.4.1/lib/p5.min.js"></script>
目标： 我有一个三角球。球具有初始位置和速度。我想弄清楚球会击中三角形的哪一侧。
我试过的： 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
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>
我无法理解你的数学。我认为您应该尝试使用解释性注释来注释此类代码。这通常会帮助您发现自己的错误：
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);
这是一些工作数学。可能不是最多的dense/elegant，但是我试着从基本的代数开始一步步讲解：
// Find which of
//
// P1 to P2 = green
// P1 to P3 = purple
// P2 to P3 = blue
//
// PO to PO + V0 intersects with
// Find the intersection point between lines A and B
function intersection(Ax1, Ay1, Ax2, Ay2, Bx1, By1, Bx2, By2) {
// Calculate the slope of line A
let Am = (Ay2 - Ay1) / (Ax2 - Ax1);
// Calculate the y-intercept of line A
let Ab = Ay1 - Ax1 * Am;
// slope of line B
let Bm = (By2 - By1) / (Bx2 - Bx1);
// y-intercept of line B
let Bb = By1 - Bx1 * Bm;
if (Am === Bm) {
// Parallel lines
return;
}
if (!Number.isFinite(Am)) {
// Line A is vertical
if (!Number.isFinite(Bm)) {
// Line B is also vertical (Am may not equal Bm though because Infinity != NegativeInfinity)
return;
} else {
// Since line A is vertical, intersection point will lie along the same x position as Ax1 and Ax2
const xInt = Ax1;
// Simply use the equation for line segment B to find the corresponding Y value
const yInt = Bm * xInt + Bb;
return createVector(xInt, yInt);
}
} else if (!Number.isFinite(Bm)) {
// Line B is vertical
const xInt = Bx1;
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
} else {
// Derived from Am * x + Ab = Bm * x + Bb
const xInt = (Bb - Ab) / (Am - Bm);
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
}
}
let P1toP2int =
intersection(P1.x, P1.y, P2.x, P2.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P1toP3int =
intersection(P1.x, P1.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P2toP3int =
intersection(P2.x, P2.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
// These intersection points assume that all lines point infinitely in both
// directions, so we still have some more work to do.
// Check if each of these points is within the target segment
function isWithin(lineX1, lineY1, lineX2, lineY2, xInt, yInt) {
if (abs((lineY2 - lineY1) / (lineX2 - lineX1)) > 1) {
// If the line segment is more vertical, check the Y position
return yInt >= min(lineY1, lineY2) && yInt <= max(lineY1, lineY2);
} else {
return xInt >= min(lineX1, lineX2) && xInt <= max(lineX1, lineX2);
}
}
if (P1toP2int && !isWithin(P1.x, P1.y, P2.x, P2.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isWithin(P1.x, P1.y, P3.x, P3.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isWithin(P2.x, P2.y, P3.x, P3.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
// Check if each intersection point is in the direction our ray is pointing
function isOnRay(rayX0, rayY0, rayX1, rayY1, xInt, yInt) {
// If the ray is more vertical, check the y coordinates
if (abs((rayY1 - rayY0) / (rayX1 - rayX0)) > 1) {
// If the ray is pointing in the positive Y direction
// (rayY1 > rayY0) then the yInt must be on the positive
// side of rayY0; and vice versa
return (rayY1 > rayY0) === (yInt > rayY0);
} else {
return (rayX1 > rayX0) === (xInt > rayX0);
}
}
if (P1toP2int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
let angle = 0;
let sides = [];
let vertices = [];
const len = 100;
let angleOne;
let angleTwo;
let angleThree;
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");
angleThree = createSlider(0, 360, 0);
angleThree.position(10, 50);
angleThree.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();
let rayAngle = angleThree.value();
fill(0);
strokeWeight(0);
textSize(15);
text(angOne, 100, 25);
text(angTwo, 100, 45);
text(rayAngle, 100, 65);
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[4].a.x,
vertices[4].a.y,
"blue"
);
sides[5] = new Side(
vertices[0].a.x,
vertices[0].a.y,
vertices[4].a.x,
vertices[4].a.y,
"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 P1 = vertices[0].a;
let P2 = vertices[1].a;
let P3 = vertices[4].a;
stroke(255, 255, 0);
stroke("purple"); // Change the color
strokeWeight(5); // Make the points 10 pixels in size
let P0 = createVector(P1.x + 60, P1.y - 40);
let V0 = createVector(15 * cos(rayAngle), 15 * sin(rayAngle));
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);
// Find which of
//
// P1 to P2 = green
// P1 to P3 = purple
// P2 to P3 = blue
//
// PO to PO + V0 intersects with
// Find the intersection point between lines A and B
function intersection(Ax1, Ay1, Ax2, Ay2, Bx1, By1, Bx2, By2) {
// Calculate the slope of line A
let Am = (Ay2 - Ay1) / (Ax2 - Ax1);
// Calculate the y-intercept of line A
let Ab = Ay1 - Ax1 * Am;
// slope of line B
let Bm = (By2 - By1) / (Bx2 - Bx1);
// y-intercept of line B
let Bb = By1 - Bx1 * Bm;
if (Am === Bm) {
// Parallel lines
return;
}
if (!Number.isFinite(Am)) {
// Line A is vertical
if (!Number.isFinite(Bm)) {
// Line B is also vertical (Am may not equal Bm though because Infinity != NegativeInfinity)
return;
} else {
// Since line A is vertical, intersection point will lie along the same x position as Ax1 and Ax2
const xInt = Ax1;
// Simply use the equation for line segment B to find the corresponding Y value
const yInt = Bm * xInt + Bb;
return createVector(xInt, yInt);
}
} else if (!Number.isFinite(Bm)) {
// Line B is vertical
const xInt = Bx1;
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
} else {
// Derived from Am * x + Ab = Bm * x + Bb
const xInt = (Bb - Ab) / (Am - Bm);
const yInt = Am * xInt + Ab;
return createVector(xInt, yInt);
}
}
let P1toP2int =
intersection(P1.x, P1.y, P2.x, P2.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P1toP3int =
intersection(P1.x, P1.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
let P2toP3int =
intersection(P2.x, P2.y, P3.x, P3.y, P0.x, P0.y, P0.x + V0.x, P0.y + V0.y);
// These intersection points assume that all lines point infinitely in both
// directions, so we still have some more work to do.
// Check if each of these points is within the target segment
function isWithin(lineX1, lineY1, lineX2, lineY2, xInt, yInt) {
if (abs((lineY2 - lineY1) / (lineX2 - lineX1)) > 1) {
// If the line segment is more vertical, check the Y position
return yInt >= min(lineY1, lineY2) && yInt <= max(lineY1, lineY2);
} else {
return xInt >= min(lineX1, lineX2) && xInt <= max(lineX1, lineX2);
}
}
if (P1toP2int && !isWithin(P1.x, P1.y, P2.x, P2.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isWithin(P1.x, P1.y, P3.x, P3.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isWithin(P2.x, P2.y, P3.x, P3.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
// Check if each intersection point is in the direction our ray is pointing
function isOnRay(rayX0, rayY0, rayX1, rayY1, xInt, yInt) {
// If the ray is more vertical, check the y coordinates
if (abs((rayY1 - rayY0) / (rayX1 - rayX0)) > 1) {
// If the ray is pointing in the positive Y direction
// (rayY1 > rayY0) then the yInt must be on the positive
// side of rayY0; and vice versa
return (rayY1 > rayY0) === (yInt > rayY0);
} else {
return (rayX1 > rayX0) === (xInt > rayX0);
}
}
if (P1toP2int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP2int.x, P1toP2int.y)) {
P1toP2int = undefined;
}
if (P1toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P1toP3int.x, P1toP3int.y)) {
P1toP3int = undefined;
}
if (P2toP3int && !isOnRay(P0.x, P0.y, P0.x + V0.x, P0.y + V0.y, P2toP3int.x, P2toP3int.y)) {
P2toP3int = undefined;
}
// Only one of these should be true, except perhaps if the ray passes precisely through a corner
if (P1toP2int) {
stroke("Red");
strokeWeight(8);
point(P1toP2int.x, P1toP2int.y);
fill("Green");
noStroke();
text("Hit Green", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
}
if (P1toP3int) {
stroke("Red");
strokeWeight(8);
point(P1toP3int.x, P1toP3int.y);
fill("Purple");
noStroke();
text("Hit Purple", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
}
if (P2toP3int) {
stroke("Red");
strokeWeight(8);
point(P2toP3int.x, P2toP3int.y);
fill("Blue");
noStroke();
text("Hit Blue", vertices[1].a.x + 50, max(50, vertices[1].a.y - 50));
}
/* I don't understand this math at all
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>
一条射线(R1, R2)和一条线(L1, L2)的交点可以用Dot Product计算：
N = (L1.y - L2.y, L2.x - L1.x)
t = dot(R1-L1, N) / dot(L2-L1, N)
X = R1 + (R2-R1) * t (if 0 <= t <= 1 and dot(R2-R1, X-R1) > 0)
在p5.js中可以使用p5.Vector:
function intersect_ray_line_segment(r1, r2, l1, l2) {
let R = p5.Vector.sub(r2, r1);
let L = p5.Vector.sub(l2, l1);
let N = p.createVector(-R.y, R.x);
if (L.dot(N) == 0) {
return undefined; // parallel
}
let t = p5.Vector.sub(r1, l1).dot(N) / L.dot(N);
if (t < 0 || t > 1) {
return undefined; // intersection is not on line segment
}
let X = L.mult(t).add(l1);
if (R.dot(p5.Vector.sub(X, r1)) < 0) {
return undefined; // wrong direction
}
return X;
}
示例：
var sketch = function( p ) {
p.setup = function() {
let sketchCanvas = p.createCanvas(p.windowWidth, p.windowHeight);
}
p.windowResized = function() {
p.resizeCanvas(p.windowWidth, p.windowHeight);
}
function intersect_ray_line_segment(r1, r2, l1, l2) {
let R = p5.Vector.sub(r2, r1);
let L = p5.Vector.sub(l2, l1);
let N = p.createVector(-R.y, R.x);
if (L.dot(N) == 0) {
return undefined; // parallel
}
let t = p5.Vector.sub(r1, l1).dot(N) / L.dot(N);
if (t < 0 || t > 1) {
return undefined; // intersection is not on line segment
}
let X = L.mult(t).add(l1);
if (R.dot(p5.Vector.sub(X, r1)) < 0) {
return undefined; // wrong direction
}
return X;
}
function closest_hit_point(r1, r2, points, lines) {
let hit_p = undefined;
let dist = undefined;
let N = undefined;
for (let i = 0; i < lines.length; ++i) {
let l1 = points[lines[i][0]];
let l2 = points[lines[i][1]];
let new_hit_p = intersect_ray_line_segment(r1, r2, points[lines[i][0]], points[lines[i][1]]);
if (new_hit_p) {
let new_d = p5.Vector.dist(r1, new_hit_p);
if (new_d > 0.1 && (!dist || new_d < dist)) {
dist = new_d;
hit_p = new_hit_p;
N = p.createVector(l1.y - l2.y, l2.x - l1.x);
}
}
}
return hit_p ? [hit_p, N] : undefined;
}
p.draw = function() {
let sx = p.width / 2;
let sy = p.height / 2;
let points = [
p.createVector(-sx*0.7, -sy*0.2), p.createVector(-sx*0.7, +sy*0.2),
p.createVector(-sx*0.3, -sy*0.5), p.createVector(sx*0.4, -sy*0.5),
p.createVector(sx*0.6, -sy*0.3), p.createVector(sx*0.6, sy*0.5), p.createVector(-sx*0.3, sy*0.5)];
let lines = [[0, 1], [2, 3], [3, 4], [4, 5], [5, 6]]
let center = new p5.Vector(0, 0);
let mouse_p = p.createVector(p.mouseX - sx, p.mouseY - sy);
let direction = p.createVector(mouse_p.x - center.x, mouse_p.y - center.y);
let hit_points = [center]
if (center.x != mouse_p.x || center.y != mouse_p.y) {
let start = center;
result = closest_hit_point(center, mouse_p, points, lines);
let count = 0
while (result && count < 100) {
hit_points.push(result[0]);
direction = direction.reflect(result[1]);
result = closest_hit_point(result[0], p5.Vector.add(result[0], direction), points, lines);
count ++;
}
}
direction.normalize();
hit_points.push(direction.mult( new p5.Vector(p.width, p.height).mag()).add(hit_points[hit_points.length-1]));
p.translate(p.width/2, p.height/2);
p.background(192);
p.strokeWeight(3);
p.stroke(64, 64, 255);
p.fill(128, 128, 255);
for (let i = 0; i < lines.length; ++i) {
let p0 = points[lines[i][0]];
let p1 = points[lines[i][1]];
p.line(p0.x, p0.y, p1.x, p1.y);
}
for (let i = 0; i < points.length; ++i) {
p.ellipse(points[i].x, points[i].y, 10, 10);
}
p.stroke(0, 0, 0);
p.fill(128, 128, 128);
p.ellipse(center.x, center.y, 10, 10);
for (let i = 1; i < hit_points.length; ++i) {
p.line(hit_points[i-1].x, hit_points[i-1].y, hit_points[i].x, hit_points[i].y);
}
for (let i = 0; i < hit_points.length; ++i) {
p.ellipse(hit_points[i].x, hit_points[i].y, 10, 10);
}
}
};
var circle_3_pts = new p5(sketch);
<script src="https://cdn.jsdelivr.net/npm/p5@1.4.1/lib/p5.min.js"></script>