Mini 2D physics

febuary 2019

A tiny 2D physics engine made in JS, featuring circles and rectangles.

Inspired by this book and the corresponding source code.

My goal was to make it as short as possible but still readable and hackable by anyone, to add features for example.

It weighs 1.57kb minified and zipped.

- Github

- Commented source code

- Demo

- emojysics JS1k entry based on this project

t=(r,a)=>({x:r,y:a}),M=r=>h(r,r)**.5,o=(r,a)=>t(r.x+a.x,r.y+a.y),n=(r,a)=>o(r,e(a,-1)),e=(r,a)=>t(r.x*a,r.y*a),h=(r,a)=>r.x*a.x+r.y*a.y,f=(r,a)=>r.x*a.y-r.y*a.x,v=(r,a,M,o=r.x-a.x,n=r.y-a.y)=>t(o*Math.cos(M)-n*Math.sin(M)+a.x,o*Math.sin(M)+n*Math.cos(M)+a.y),i=r=>e(r,1/(M(r)||1)),y=t(0,100),N=[],x={},B={},d={},m=(r,a,t,M)=>{r.D=a,r.N=t,r.S=M,r.E=o(M,e(t,a))},s=(r,a,M,o,n,e,h,f,v)=>(v={T:n,C:r,F:M,R:o,M:a?1/a:0,V:t(0,0),A:a?y:t(0,0),G:0,v:0,a:0,B:e,W:h,H:f,I:n?(Math.hypot(h,f),a>0?1/(a*(h**2+f**2)/12):0):a>0?a*e**2/12:0,N:[],X:[t(r.x-h/2,r.y-f/2),t(r.x+h/2,r.y-f/2),t(r.x+h/2,r.y+f/2),t(r.x-h/2,r.y+f/2)]},n&&T(v),N.push(v),v),C=(r,a,t)=>{if(r.C=o(r.C,a),r.T)for(t=4;t--;)r.X[t]=o(r.X[t],a)},X=(r,a,t)=>{if(r.G+=a,r.T){for(t=4;t--;)r.X[t]=v(r.X[t],r.C,a);T(r)}},V=(r,a)=>M(n(a.C,r.C))<=r.B+a.B,T=(r,a)=>{for(a=4;a--;)r.N[a]=i(n(r.X[(a+1)%4],r.X[(a+2)%4]))},l=(r,a,t)=>{var M,f,v,i,y,N,x=1e9,B=-1,d=1;for(f=4;d&&f--;){M=r.N[f];var c,s,C=e(M,-1),X=r.X[f];for(N=-1e9,y=-1,v=4;v--;)c=n(a.X[v],X),(s=h(c,C))>0&&s>N&&(y=a.X[v],N=s);(d=-1!==y)&&N{if(!r.T&&!a.T){var f=n(a.C,r.C),v=r.B+a.B,y=M(f);if(y<=Math.sqrt(v*v)){var N=i(e(f,-1)),c=e(N,a.B);m(x,v-y,i(f),o(a.C,c))}return 1}if(r.T&&a.T){var s,C=0;return(s=l(r,a,B))&&(C=l(a,r,d))&&(B.D0){g=I,E=X,S=0;break}I>g&&(g=I,E=X)}if(S)m(x,a.B-g,r.N[E],n(T,e(r.N[E],a.B)));else{var R=n(T,r.X[E]),k=n(r.X[(E+1)%4],r.X[E]),p=h(R,k);if(p<0){if((u=M(R))>a.B)return;D=i(R),m(x,a.B-u,D,o(T,e(D,-a.B)))}else if(R=n(T,r.X[(E+1)%4]),k=e(k,-1),(p=h(R,k))<0){if((u=M(R))>a.B)return;D=i(R),m(x,a.B-u,D,o(T,e(D,-a.B)))}else{if(!(g{if(r.M||a.M){var v=M.D/(r.M+a.M)*.8,y=e(M.N,v),N=M.N;C(r,e(y,-r.M)),C(a,e(y,a.M));var x=e(M.S,a.M/(r.M+a.M)),B=e(M.E,r.M/(r.M+a.M)),d=o(x,B),m=n(d,r.C),c=n(d,a.C),s=o(r.V,t(-1*r.v*m.y,r.v*m.x)),X=o(a.V,t(-1*a.v*c.y,a.v*c.x)),V=n(X,s),T=h(V,N);if(!(T>0)){var l=Math.min(r.R,a.R),I=Math.min(r.F,a.F),u=f(m,N),D=f(c,N),S=-(1+l)*T/(r.M+a.M+u*u*r.I+D*D*a.I),g=e(N,S);r.V=n(r.V,e(g,r.M)),a.V=o(a.V,e(g,a.M)),r.v-=u*S*r.I,a.v+=D*S*a.I;var E=e(i(n(V,e(N,h(V,N)))),-1),R=f(m,E),k=f(c,E),p=-(1+l)*h(V,E)*I/(r.M+a.M+R*R*r.I+k*k*a.I);p>S&&(p=S),g=e(E,p),r.V=n(r.V,e(g,r.M)),a.V=o(a.V,e(g,a.M)),r.v-=R*p*r.I,a.v+=k*p*a.I}}};setInterval((r,t,M)=>{for(a.width^=0,M=9;M--;)for(r=N.length;r--;)for(t=N.length;t-->r;)V(N[r],N[t])&&I(N[r],N[t])&&(h(x.N,n(N[t].C,N[r].C))<0&&(x={D:x.D,N:e(x.N,-1),S:x.E,E:x.S}),u(N[r],N[t],x));for(r=N.length;r--;)c.save(),c.translate(N[r].C.x,N[r].C.y),c.rotate(N[r].G),N[r].T?c.strokeRect(-N[r].W/2,-N[r].H/2,N[r].W,N[r].H):(c.beginPath(),c.arc(0,0,N[r].B,0,7),c.lineTo(0,0),c.closePath(),c.stroke()),c.restore(),N[r].V=o(N[r].V,e(N[r].A,1/60)),C(N[r],e(N[r].V,1/60)),N[r].v+=1*N[r].a/60,X(N[r],1*N[r].v/60)},16);var D=(r,a,t,M,o)=>s(r,t,M,o,0,a),S=(r,a,t,M,o,n)=>s(r,M,o,n,1,Math.hypot(a,t)/2,a,t)