所以我写了一个微生物动画。
一切都很酷，但我认为如果微生物能够吃硅藻并破坏气泡，那就更好了。
问题是微生物是由贝塞尔曲线构成的。
我不知道如何以合理的方式检查由贝塞尔曲线构成的对象与圆之间的碰撞。
我唯一想到的是绘制微生物形状并在隐藏的 Canvas 上冒泡，然后检查它们是否绘制到相同的像素。但这会引起恕我直言的重大性能问题。
代码:https://codepen.io/michaelKurowski/pen/opWeKYclass Cell 是单元格，而 class CellWallNode 是贝塞尔曲线的一个节点，以防有人需要查找实现。
气泡和硅藻可以很容易地简化为圆形。
最佳答案
贝塞尔曲线定义的边界测试对象的解决方案
下面是一个示例解决方案，用于查找圆是否位于由中心点和一组定义周长的贝塞尔曲线定义的对象内。
该解决方案仅针对不相交的三次贝塞尔曲线进行了测试。如果被测物体和单元中心之间有两个以上的截距，也将不起作用。但是，您需要解决更复杂的边界的所有内容都在代码中。
方法
line 笔记
测试是沿着一条线到中心的点，而不是圆，圆是由三 Angular 形定义的区域。只要与贝塞尔曲线的大小相比，圆半径较小，近似就可以很好地工作。
不确定您使用的是三次贝塞尔曲线还是二次贝塞尔曲线，因此该解决方案涵盖了三次贝塞尔曲线和二次贝塞尔曲线。
例子
该代码段围绕中心点创建了一组贝塞尔曲线(三次方)。对象
theBlob 包含动画贝塞尔曲线。函数testBlob测试鼠标的位置，如果在theBlob内部，则返回true。对象 bezHelper 包含解决问题所需的所有功能。立方根求解器源自 github intersections 立方根求解器。
const bezHelper = (()=>{
// creates a 2D point
const P2 = (x=0, y= x === 0 ? 0 : x.y + (x = x.x, 0)) => ({x, y});
const setP2As = (p,pFrom) => (p.x = pFrom.x, p.y = pFrom.y, p);
// To prevent heap thrashing close over some pre defined 2D points
const v1 = P2();
const v2 = P2();
const v3 = P2();
const v4 = P2();
var u,u1,u2;
// solves quadratic for bezier 2 returns first root
function solveBezier2(A, B, C){
// solve the 2nd order bezier equation.
// There can be 2 roots, u,u1 hold the results;
// 2nd order function a+2(-a+b)x+(a-2b+c)x^2
a = (A - 2 * B + C);
b = 2 * ( - A + B);
c = A;
a1 = 2 * a;
c = b * b - 4 * a * c;
if(c < 0){
u = Infinity;
u1 = Infinity;
return u;
}else{
b1 = Math.sqrt(c);
}
u = (-b + b1) / a1;
u1 = (-b - b1) / a1;
return u;
}
// solves cubic for bezier 3 returns first root
function solveBezier3(A, B, C, D){
// There can be 3 roots, u,u1,u2 hold the results;
// Solves 3rd order a+(-2a+3b)t+(2a-6b+3c)t^2+(-a+3b-3c+d)t^3 Cardano method for finding roots
// this function was derived from http://pomax.github.io/bezierinfo/#intersections cube root solver
// Also see https://en.wikipedia.org/wiki/Cubic_function#Cardano.27s_method
function crt(v) {
if(v<0) return -Math.pow(-v,1/3);
return Math.pow(v,1/3);
}
function sqrt(v) {
if(v<0) return -Math.sqrt(-v);
return Math.sqrt(v);
}
var a, b, c, d, p, p3, q, q2, discriminant, U, v1, r, t, mp3, cosphi,phi, t1, sd;
u2 = u1 = u = -Infinity;
d = (-A + 3 * B - 3 * C + D);
a = (3 * A - 6 * B + 3 * C) / d;
b = (-3 * A + 3 * B) / d;
c = A / d;
p = (3 * b - a * a) / 3;
p3 = p / 3;
q = (2 * a * a * a - 9 * a * b + 27 * c) / 27;
q2 = q / 2;
a /= 3;
discriminant = q2 * q2 + p3 * p3 * p3;
if (discriminant < 0) {
mp3 = -p / 3;
r = sqrt(mp3 * mp3 * mp3);
t = -q / (2 * r);
cosphi = t < -1 ? -1 : t > 1 ? 1 : t;
phi = Math.acos(cosphi);
t1 = 2 * crt(r);
u = t1 * Math.cos(phi / 3) - a;
u1 = t1 * Math.cos((phi + 2 * Math.PI) / 3) - a;
u2 = t1 * Math.cos((phi + 4 * Math.PI) / 3) - a;
return u;
}
if(discriminant === 0) {
U = q2 < 0 ? crt(-q2) : -crt(q2);
u = 2 * U - a;
u1 = -U - a;
return u;
}
sd = sqrt(discriminant);
u = crt(sd - q2) - crt(sd + q2) - a;
return u;
}
// get a point on the bezier at pos ( from 0 to 1 values outside this range will be outside the bezier)
// p1, p2 are end points and cp1, cp2 are control points.
// ret is the resulting point. If given it is set to the result, if not given a new point is created
function getPositionOnBez(pos,p1,p2,cp1,cp2,ret = P2()){
if(pos === 0){
ret.x = p1.x;
ret.y = p1.y;
return ret;
}else
if(pos === 1){
ret.x = p2.x;
ret.y = p2.y;
return ret;
}
v1.x = p1.x;
v1.y = p1.y;
var c = pos;
if(cp2 === undefined){
v2.x = cp1.x;
v2.y = cp1.y;
v1.x += (v2.x - v1.x) * c;
v1.y += (v2.y - v1.y) * c;
v2.x += (p2.x - v2.x) * c;
v2.y += (p2.y - v2.y) * c;
ret.x = v1.x + (v2.x - v1.x) * c;
ret.y = v1.y + (v2.y - v1.y) * c;
return ret;
}
v2.x = cp1.x;
v2.y = cp1.y;
v3.x = cp2.x;
v3.y = cp2.y;
v1.x += (v2.x - v1.x) * c;
v1.y += (v2.y - v1.y) * c;
v2.x += (v3.x - v2.x) * c;
v2.y += (v3.y - v2.y) * c;
v3.x += (p2.x - v3.x) * c;
v3.y += (p2.y - v3.y) * c;
v1.x += (v2.x - v1.x) * c;
v1.y += (v2.y - v1.y) * c;
v2.x += (v3.x - v2.x) * c;
v2.y += (v3.y - v2.y) * c;
ret.x = v1.x + (v2.x - v1.x) * c;
ret.y = v1.y + (v2.y - v1.y) * c;
return ret;
}
const cubicBez = 0;
const quadraticBez = 1;
const none = 2;
var type = none;
// working bezier
const p1 = P2();
const p2 = P2();
const cp1 = P2();
const cp2 = P2();
// rotated bezier
const rp1 = P2();
const rp2 = P2();
const rcp1 = P2();
const rcp2 = P2();
// translate and rotate bezier
function transformBez(pos,rot){
const ax = Math.cos(rot);
const ay = Math.sin(rot);
var x = p1.x - pos.x;
var y = p1.y - pos.y;
rp1.x = x * ax - y * ay;
rp1.y = x * ay + y * ax;
x = p2.x - pos.x;
y = p2.y - pos.y;
rp2.x = x * ax - y * ay;
rp2.y = x * ay + y * ax;
x = cp1.x - pos.x;
y = cp1.y - pos.y;
rcp1.x = x * ax - y * ay;
rcp1.y = x * ay + y * ax;
if(type === cubicBez){
x = cp2.x - pos.x;
y = cp2.y - pos.y;
rcp2.x = x * ax - y * ay;
rcp2.y = x * ay + y * ax;
}
}
function getPosition2(pos,ret){
return getPositionOnBez(pos,p1,p2,cp1,undefined,ret);
}
function getPosition3(pos,ret){
return getPositionOnBez(pos,p1,p2,cp1,cp2,ret);
}
const API = {
getPosOnQBez(pos,p1,cp1,p2,ret){
return getPositionOnBez(pos,p1,p2,cp1,undefined,ret);
},
getPosOnCBez(pos,p1,cp1,cp2,p2,ret){
return getPositionOnBez(pos,p1,p2,cp1,cp2,ret);
},
set bezQ(points){
setP2As(p1, points[0]);
setP2As(cp1, points[1]);
setP2As(p2, points[2]);
type = quadraticBez;
},
set bezC(points){
setP2As(p1, points[0]);
setP2As(cp1, points[1]);
setP2As(cp2, points[2]);
setP2As(p2, points[3]);
type = cubicBez;
},
isInside(center, testPoint, pointRadius){
drawLine(testPoint , center);
v1.x = (testPoint.x - center.x);
v1.y = (testPoint.y - center.y);
const pointDist = Math.sqrt(v1.x * v1.x + v1.y * v1.y)
const dir = -Math.atan2(v1.y,v1.x);
transformBez(center,dir);
if(type === cubicBez){
solveBezier3(rp1.y, rcp1.y, rcp2.y, rp2.y);
if (u < 0 || u > 1) { u = u1 }
if (u < 0 || u > 1) { u = u2 }
if (u < 0 || u > 1) { return }
getPosition3(u, v4);
}else{
solveBezier2(rp1.y, rcp1.y, rp2.y);
if (u < 0 || u > 1) { u = u1 }
if (u < 0 || u > 1) { return }
getPosition2(u, v4);
}
drawCircle(v4);
const dist = Math.sqrt((v4.x - center.x) ** 2 + (v4.y - center.y) ** 2);
const dist1 = Math.sqrt((v4.x - testPoint.x) ** 2 + (v4.y - testPoint.y) ** 2);
return dist1 < dist && dist > pointDist - pointRadius;
}
}
return API;
})();
const ctx = canvas.getContext("2d");
const m = {x : 0, y : 0};
document.addEventListener("mousemove",e=>{
var b = canvas.getBoundingClientRect();
m.x = e.pageX - b.left - scrollX - 2;
m.y = e.pageY - b.top - scrollY - 2;
});
function drawCircle(p,r = 5,col = "black"){
ctx.beginPath();
ctx.strokeStyle = col;
ctx.arc(p.x,p.y,r,0,Math.PI*2)
ctx.stroke();
}
function drawLine(p1,p2,r = 5,col = "black"){
ctx.beginPath();
ctx.strokeStyle = col;
ctx.lineTo(p1.x,p1.y);
ctx.lineTo(p2.x,p2.y);
ctx.stroke();
}
const w = 400;
const h = 400;
const diag = Math.sqrt(w * w + h * h);
// creates a 2D point
const P2 = (x=0, y= x === 0 ? 0 : x.y + (x = x.x, 0)) => ({x, y});
const setP2As = (p,pFrom) => (p.x = pFrom.x, p.y = pFrom.y, p);
// random int and double
const randI = (min, max = min + (min = 0)) => (Math.random()*(max - min) + min) | 0;
const rand = (min = 1, max = min + (min = 0)) => Math.random() * (max - min) + min;
const theBlobSet = [];
const theBlob = [];
function createCubicBlob(segs){
const step = Math.PI / segs;
for(var i = 0; i < Math.PI * 2; i += step){
const dist = rand(diag * (1/6), diag * (1/5));
const ang = i + rand(-step * 0.2,step * 0.2);
const p = P2(
w / 2 + Math.cos(ang) * dist,
h / 2 + Math.sin(ang) * dist
);
theBlobSet.push(p);
theBlob.push(P2(p));
}
theBlobSet[theBlobSet.length -1] = theBlobSet[0];
theBlob[theBlobSet.length -1] = theBlob[0];
}
createCubicBlob(8);
function animateTheBlob(time){
for(var i = 0; i < theBlobSet.length-1; i++){
const ang = Math.sin(time + i) * 6;
theBlob[i].x = theBlobSet[i].x + Math.cos(ang) * diag * 0.04;
theBlob[i].y = theBlobSet[i].y + Math.sin(ang) * diag * 0.04;
}
}
function drawTheBlob(){
ctx.strokeStyle = "black";
ctx.lineWidth = 3;
ctx.beginPath();
var i = 0;
ctx.moveTo(theBlob[i].x,theBlob[i++].y);
while(i < theBlob.length){
ctx.bezierCurveTo(
theBlob[i].x,theBlob[i++].y,
theBlob[i].x,theBlob[i++].y,
theBlob[i].x,theBlob[i++].y
);
}
ctx.stroke();
}
var center = P2(w/2,h/2);
function testBlob(){
var i = 0;
while(i < theBlob.length-3){
bezHelper.bezC = [theBlob[i++], theBlob[i++], theBlob[i++], theBlob[i]];
if(bezHelper.isInside(center,m,6)){
return true;
}
}
return false;
}
// main update function
function update(timer){
ctx.clearRect(0,0,w,h);
animateTheBlob(timer/1000)
drawTheBlob();
if(testBlob()){
ctx.strokeStyle = "red";
}else{
ctx.strokeStyle = "black";
}
ctx.beginPath();
ctx.arc(m.x,m.y,5,0,Math.PI*2)
ctx.stroke();
requestAnimationFrame(update);
}
requestAnimationFrame(update);canvas { border : 2px solid black; }<canvas id="canvas" width = "400" height = "400"></canvas>关于javascript - 如何检测由贝塞尔曲线和圆组成的对象之间的碰撞？，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/48034420/