0hmX/am3352

scripts/ddr-spacing-intervals.ts

export type SpacingPoint={x:number;y:number}
export type SpacingInterval=[number,number]
export function unionSpacingIntervals(intervals:SpacingInterval[]):SpacingInterval[]{
 const sorted=intervals.filter(([a,b])=>b>a+1e-12).map(([a,b])=>[Math.max(0,a),Math.min(1,b)]as SpacingInterval).sort((a,b)=>a[0]-b[0]),out:SpacingInterval[]=[]
 for(const [a,b]of sorted){if(b<=a)continue;const last=out.at(-1);if(last&&a<=last[1]+1e-10)last[1]=Math.max(last[1],b);else out.push([a,b])}return out
}
/** Exact subject fractions lying within the radius of a finite segment.
 * Split at projections onto the other segment's endpoints, then solve the
 * appropriate line-strip or endpoint-circle quadratic. */
export function segmentProximityIntervals(a:SpacingPoint,b:SpacingPoint,c:SpacingPoint,d:SpacingPoint,radius:number):SpacingInterval[]{
 if(![a.x,a.y,b.x,b.y,c.x,c.y,d.x,d.y,radius].every(Number.isFinite)||radius<=0)throw Error('Finite positive spacing geometry required')
 const vx=b.x-a.x,vy=b.y-a.y,wx=d.x-c.x,wy=d.y-c.y,l2=wx*wx+wy*wy,v2=vx*vx+vy*vy
 if(v2<1e-20)return []
 const u0=l2?((a.x-c.x)*wx+(a.y-c.y)*wy)/l2:0,u1=l2?(vx*wx+vy*wy)/l2:0,cuts=[0,1]
 if(Math.abs(u1)>1e-15)for(const u of[0,1]){const t=(u-u0)/u1;if(t>0&&t<1)cuts.push(t)}cuts.sort((a,b)=>a-b)
 const out:SpacingInterval[]=[]
 for(let i=1;i<cuts.length;i++){
  const lo=cuts[i-1]!,hi=cuts[i]!,u=u0+u1*(lo+hi)/2;let A:number,B:number,C:number
  if(!l2||u<0||u>1){const p=u>1?d:c,px=a.x-p.x,py=a.y-p.y;A=v2;B=2*(px*vx+py*vy);C=px*px+py*py-radius*radius}
  else{const k0=wx*(a.y-c.y)-wy*(a.x-c.x),k1=wx*vy-wy*vx;A=k1*k1;B=2*k0*k1;C=k0*k0-radius*radius*l2}
  if(A<1e-20){if(C<0)out.push([lo,hi]);continue}
  const discriminant=B*B-4*A*C;if(discriminant<=0)continue
  const root=Math.sqrt(discriminant),start=Math.max(lo,(-B-root)/(2*A)),end=Math.min(hi,(-B+root)/(2*A));if(end>start)out.push([start,end])
 }
 return unionSpacingIntervals(out)
}