From 83c00fa87d1b17284175f7d5fd2a0350153ddc43 Mon Sep 17 00:00:00 2001
From: xigua <hhbuhuiai@163.com>
Date: Sun, 4 Aug 2024 15:50:15 +0800
Subject: [PATCH] optimize utils.droots

---
 dist/bezier.cjs   |  6 +++++-
 dist/bezier.js    |  2 +-
 package-lock.json | 26 +++++++++++++++++++-------
 src/utils.js      |  6 +++++-
 4 files changed, 30 insertions(+), 10 deletions(-)

diff --git a/dist/bezier.cjs b/dist/bezier.cjs
index efc021d..9db9e2d 100644
--- a/dist/bezier.cjs
+++ b/dist/bezier.cjs
@@ -478,7 +478,11 @@ var utils = {
     if (p.length === 3) {
       const a = p[0], b = p[1], c = p[2], d = a - 2 * b + c;
       if (d !== 0) {
-        const m1 = -sqrt(b * b - a * c), m2 = -a + b, v1 = -(m1 + m2) / d, v2 = -(-m1 + m2) / d;
+        const m1Pow2 = b * b - a * c;
+        if (m1Pow2 < 0) {
+          return [];
+        }
+        const m1 = -sqrt(m1Pow2), m2 = -a + b, v1 = -(m1 + m2) / d, v2 = -(-m1 + m2) / d;
         return [v1, v2];
       } else if (b !== c && d === 0) {
         return [(2 * b - c) / (2 * (b - c))];
diff --git a/dist/bezier.js b/dist/bezier.js
index dea91ec..5312d06 100644
--- a/dist/bezier.js
+++ b/dist/bezier.js
@@ -1 +1 @@
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r={x:i.y*e.z-i.z*e.y,y:i.z*e.x-i.x*e.z,z:i.x*e.y-i.y*e.x},u=X(r.x*r.x+r.y*r.y+r.z*r.z);r.x/=u,r.y/=u,r.z/=u;let f=[r.x*r.x,r.x*r.y-r.z,r.x*r.z+r.y,r.x*r.y+r.z,r.y*r.y,r.y*r.z-r.x,r.x*r.z-r.y,r.y*r.z+r.x,r.z*r.z];return{t:n,x:f[0]*e.x+f[1]*e.y+f[2]*e.z,y:f[3]*e.x+f[4]*e.y+f[5]*e.z,z:f[6]*e.x+f[7]*e.y+f[8]*e.z}}hull(n){let e=this.points,i=[],s=[],o=0;for(s[o++]=e[0],s[o++]=e[1],s[o++]=e[2],this.order===3&&(s[o++]=e[3]);e.length>1;){i=[];for(let r=0,u,f=e.length-1;r<f;r++)u=h.lerp(n,e[r],e[r+1]),s[o++]=u,i.push(u);e=i}return s}split(n,e){if(n===0&&!!e)return this.split(e).left;if(e===1)return this.split(n).right;let i=this.hull(n),s={left:this.order===2?new v([i[0],i[3],i[5]]):new v([i[0],i[4],i[7],i[9]]),right:this.order===2?new v([i[5],i[4],i[2]]):new v([i[9],i[8],i[6],i[3]]),span:i};return s.left._t1=h.map(0,0,1,this._t1,this._t2),s.left._t2=h.map(n,0,1,this._t1,this._t2),s.right._t1=h.map(n,0,1,this._t1,this._t2),s.right._t2=h.map(1,0,1,this._t1,this._t2),e?(e=h.map(e,n,1,0,1),s.right.split(e).left):s}extrema(){let n={},e=[];return this.dims.forEach(function(i){let s=function(r){return r[i]},o=this.dpoints[0].map(s);n[i]=h.droots(o),this.order===3&&(o=this.dpoints[1].map(s),n[i]=n[i].concat(h.droots(o))),n[i]=n[i].filter(function(r){return r>=0&&r<=1}),e=e.concat(n[i].sort(h.numberSort))}.bind(this)),n.values=e.sort(h.numberSort).filter(function(i,s){return e.indexOf(i)===s}),n}bbox(){let n=this.extrema(),e={};return this.dims.forEach(function(i){e[i]=h.getminmax(this,i,n[i])}.bind(this)),e}overlaps(n){let e=this.bbox(),i=n.bbox();return h.bboxoverlap(e,i)}offset(n,e){if(typeof e!="undefined"){let i=this.get(n),s=this.normal(n),o={c:i,n:s,x:i.x+s.x*e,y:i.y+s.y*e};return this._3d&&(o.z=i.z+s.z*e),o}if(this._linear){let i=this.normal(0),s=this.points.map(function(o){let r={x:o.x+n*i.x,y:o.y+n*i.y};return o.z&&i.z&&(r.z=o.z+n*i.z),r});return[new v(s)]}return this.reduce().map(function(i){return i._linear?i.offset(n)[0]:i.scale(n)})}simple(){if(this.order===3){let s=h.angle(this.points[0],this.points[3],this.points[1]),o=h.angle(this.points[0],this.points[3],this.points[2]);if(s>0&&o<0||s<0&&o>0)return!1}let n=this.normal(0),e=this.normal(1),i=n.x*e.x+n.y*e.y;return this._3d&&(i+=n.z*e.z),G(it(i))<rt/3}reduce(){let n,e=0,i=0,s=.01,o,r=[],u=[],f=this.extrema().values;for(f.indexOf(0)===-1&&(f=[0].concat(f)),f.indexOf(1)===-1&&f.push(1),e=f[0],n=1;n<f.length;n++)i=f[n],o=this.split(e,i),o._t1=e,o._t2=i,r.push(o),e=i;return r.forEach(function(l){for(e=0,i=0;i<=1;)for(i=e+s;i<=1+s;i+=s)if(o=l.split(e,i),!o.simple()){if(i-=s,G(e-i)<s)return[];o=l.split(e,i),o._t1=h.map(e,0,1,l._t1,l._t2),o._t2=h.map(i,0,1,l._t1,l._t2),u.push(o),e=i;break}e<1&&(o=l.split(e,1),o._t1=h.map(e,0,1,l._t1,l._t2),o._t2=l._t2,u.push(o))}),u}translate(n,e,i){i=typeof i=="number"?i:e;let s=this.order,o=this.points.map((r,u)=>(1-u/s)*e+u/s*i);return new v(this.points.map((r,u)=>({x:r.x+n.x*o[u],y:r.y+n.y*o[u]})))}scale(n){let e=this.order,i=!1;if(typeof n=="function"&&(i=n),i&&e===2)return this.raise().scale(i);let s=this.clockwise,o=this.points;if(this._linear)return this.translate(this.normal(0),i?i(0):n,i?i(1):n);let r=i?i(0):n,u=i?i(1):n,f=[this.offset(0,10),this.offset(1,10)],l=[],y=h.lli4(f[0],f[0].c,f[1],f[1].c);if(!y)throw new Error("cannot scale this curve. Try reducing it first.");return[0,1].forEach(function(a){let x=l[a*e]=h.copy(o[a*e]);x.x+=(a?u:r)*f[a].n.x,x.y+=(a?u:r)*f[a].n.y}),i?([0,1].forEach(function(a){if(!(e===2&&!!a)){var x=o[a+1],p={x:x.x-y.x,y:x.y-y.y},g=i?i((a+1)/e):n;i&&!s&&(g=-g);var _=X(p.x*p.x+p.y*p.y);p.x/=_,p.y/=_,l[a+1]={x:x.x+g*p.x,y:x.y+g*p.y}}}),new v(l)):([0,1].forEach(a=>{if(e===2&&!!a)return;let x=l[a*e],p=this.derivative(a),g={x:x.x+p.x,y:x.y+p.y};l[a+1]=h.lli4(x,g,y,o[a+1])}),new v(l))}outline(n,e,i,s){if(e=e===void 0?n:e,this._linear){let m=this.normal(0),E=this.points[0],d=this.points[this.points.length-1],z,A,k;i===void 0&&(i=n,s=e),z={x:E.x+m.x*n,y:E.y+m.y*n},k={x:d.x+m.x*i,y:d.y+m.y*i},A={x:(z.x+k.x)/2,y:(z.y+k.y)/2};let j=[z,A,k];z={x:E.x-m.x*e,y:E.y-m.y*e},k={x:d.x-m.x*s,y:d.y-m.y*s},A={x:(z.x+k.x)/2,y:(z.y+k.y)/2};let C=[k,A,z],R=h.makeline(C[2],j[0]),I=h.makeline(j[2],C[0]),K=[R,new v(j),I,new v(C)];return new P(K)}let o=this.reduce(),r=o.length,u=[],f=[],l,y=0,a=this.length(),x=typeof i!="undefined"&&typeof s!="undefined";function p(m,E,d,z,A){return function(k){let j=z/d,C=(z+A)/d,R=E-m;return h.map(k,0,1,m+j*R,m+C*R)}}o.forEach(function(m){let E=m.length();x?(u.push(m.scale(p(n,i,a,y,E))),f.push(m.scale(p(-e,-s,a,y,E)))):(u.push(m.scale(n)),f.push(m.scale(-e))),y+=E}),f=f.map(function(m){return l=m.points,l[3]?m.points=[l[3],l[2],l[1],l[0]]:m.points=[l[2],l[1],l[0]],m}).reverse();let g=u[0].points[0],_=u[r-1].points[u[r-1].points.length-1],q=f[r-1].points[f[r-1].points.length-1],O=f[0].points[0],M=h.makeline(q,g),w=h.makeline(_,O),S=[M].concat(u).concat([w]).concat(f);return new P(S)}outlineshapes(n,e,i){e=e||n;let s=this.outline(n,e).curves,o=[];for(let r=1,u=s.length;r<u/2;r++){let f=h.makeshape(s[r],s[u-r],i);f.startcap.virtual=r>1,f.endcap.virtual=r<u/2-1,o.push(f)}return o}intersects(n,e){return n?n.p1&&n.p2?this.lineIntersects(n):(n instanceof v&&(n=n.reduce()),this.curveintersects(this.reduce(),n,e)):this.selfintersects(e)}lineIntersects(n){let e=V(n.p1.x,n.p2.x),i=V(n.p1.y,n.p2.y),s=H(n.p1.x,n.p2.x),o=H(n.p1.y,n.p2.y);return h.roots(this.points,n).filter(r=>{var u=this.get(r);return h.between(u.x,e,s)&&h.between(u.y,i,o)})}selfintersects(n){let e=this.reduce(),i=e.length-2,s=[];for(let o=0,r,u,f;o<i;o++)u=e.slice(o,o+1),f=e.slice(o+2),r=this.curveintersects(u,f,n),s.push(...r);return s}curveintersects(n,e,i){let s=[];n.forEach(function(r){e.forEach(function(u){r.overlaps(u)&&s.push({left:r,right:u})})});let o=[];return s.forEach(function(r){let u=h.pairiteration(r.left,r.right,i);u.length>0&&(o=o.concat(u))}),o}arcs(n){return n=n||.5,this._iterate(n,[])}_error(n,e,i,s){let o=(s-i)/4,r=this.get(i+o),u=this.get(s-o),f=h.dist(n,e),l=h.dist(n,r),y=h.dist(n,u);return G(l-f)+G(y-f)}_iterate(n,e){let i=0,s=1,o;do{o=0,s=1;let r=this.get(i),u,f,l,y,a=!1,x=!1,p,g=s,_=1,q=0;do if(x=a,y=l,g=(i+s)/2,q++,u=this.get(g),f=this.get(s),l=h.getccenter(r,u,f),l.interval={start:i,end:s},a=this._error(l,r,i,s)<=n,p=x&&!a,p||(_=s),a){if(s>=1){if(l.interval.end=_=1,y=l,s>1){let M={x:l.x+l.r*nt(l.e),y:l.y+l.r*et(l.e)};l.e+=h.angle({x:l.x,y:l.y},M,this.get(1))}break}s=s+(s-i)/2}else s=g;while(!p&&o++<100);if(o>=100)break;y=y||l,e.push(y),i=_}while(s<1);return e}};})();
diff --git a/package-lock.json b/package-lock.json
index 7a63ea1..2ab8b92 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -8,10 +8,8 @@
       "name": "bezier-js",
       "version": "6.1.4",
       "license": "MIT",
-      "dependencies": {
-        "cross-env": "^7.0.3"
-      },
       "devDependencies": {
+        "cross-env": "^7.0.3",
         "esbuild": "^0.14.10",
         "jest": "^27.4.7",
         "npm-run-all": "^4.1.5",
@@ -1799,6 +1797,7 @@
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       "resolved": "https://registry.npmjs.org/cross-env/-/cross-env-7.0.3.tgz",
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+      "dev": true,
       "dependencies": {
         "cross-spawn": "^7.0.1"
       },
@@ -1816,6 +1815,7 @@
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       "resolved": "https://registry.npmjs.org/cross-spawn/-/cross-spawn-7.0.3.tgz",
       "integrity": "sha512-iRDPJKUPVEND7dHPO8rkbOnPpyDygcDFtWjpeWNCgy8WP2rXcxXL8TskReQl6OrB2G7+UJrags1q15Fudc7G6w==",
+      "dev": true,
       "dependencies": {
         "path-key": "^3.1.0",
         "shebang-command": "^2.0.0",
@@ -1829,6 +1829,7 @@
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       "resolved": "https://registry.npmjs.org/path-key/-/path-key-3.1.1.tgz",
       "integrity": "sha512-ojmeN0qd+y0jszEtoY48r0Peq5dwMEkIlCOu6Q5f41lfkswXuKtYrhgoTpLnyIcHm24Uhqx+5Tqm2InSwLhE6Q==",
+      "dev": true,
       "engines": {
         "node": ">=8"
       }
@@ -1837,6 +1838,7 @@
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/shebang-command/-/shebang-command-2.0.0.tgz",
       "integrity": "sha512-kHxr2zZpYtdmrN1qDjrrX/Z1rR1kG8Dx+gkpK1G4eXmvXswmcE1hTWBWYUzlraYw1/yZp6YuDY77YtvbN0dmDA==",
+      "dev": true,
       "dependencies": {
         "shebang-regex": "^3.0.0"
       },
@@ -1848,6 +1850,7 @@
       "version": "3.0.0",
       "resolved": "https://registry.npmjs.org/shebang-regex/-/shebang-regex-3.0.0.tgz",
       "integrity": "sha512-7++dFhtcx3353uBaq8DDR4NuxBetBzC7ZQOhmTQInHEd6bSrXdiEyzCvG07Z44UYdLShWUyXt5M/yhz8ekcb1A==",
+      "dev": true,
       "engines": {
         "node": ">=8"
       }
@@ -1856,6 +1859,7 @@
       "version": "2.0.2",
       "resolved": "https://registry.npmjs.org/which/-/which-2.0.2.tgz",
       "integrity": "sha512-BLI3Tl1TW3Pvl70l3yq3Y64i+awpwXqsGBYWkkqMtnbXgrMD+yj7rhW0kuEDxzJaYXGjEW5ogapKNMEKNMjibA==",
+      "dev": true,
       "dependencies": {
         "isexe": "^2.0.0"
       },
@@ -2940,7 +2944,8 @@
     "node_modules/isexe": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/isexe/-/isexe-2.0.0.tgz",
-      "integrity": "sha1-6PvzdNxVb/iUehDcsFctYz8s+hA="
+      "integrity": "sha1-6PvzdNxVb/iUehDcsFctYz8s+hA=",
+      "dev": true
     },
     "node_modules/istanbul-lib-coverage": {
       "version": "3.2.0",
@@ -7772,6 +7777,7 @@
       "version": "7.0.3",
       "resolved": "https://registry.npmjs.org/cross-env/-/cross-env-7.0.3.tgz",
       "integrity": "sha512-+/HKd6EgcQCJGh2PSjZuUitQBQynKor4wrFbRg4DtAgS1aWO+gU52xpH7M9ScGgXSYmAVS9bIJ8EzuaGw0oNAw==",
+      "dev": true,
       "requires": {
         "cross-spawn": "^7.0.1"
       },
@@ -7780,6 +7786,7 @@
           "version": "7.0.3",
           "resolved": "https://registry.npmjs.org/cross-spawn/-/cross-spawn-7.0.3.tgz",
           "integrity": "sha512-iRDPJKUPVEND7dHPO8rkbOnPpyDygcDFtWjpeWNCgy8WP2rXcxXL8TskReQl6OrB2G7+UJrags1q15Fudc7G6w==",
+          "dev": true,
           "requires": {
             "path-key": "^3.1.0",
             "shebang-command": "^2.0.0",
@@ -7789,12 +7796,14 @@
         "path-key": {
           "version": "3.1.1",
           "resolved": "https://registry.npmjs.org/path-key/-/path-key-3.1.1.tgz",
-          "integrity": "sha512-ojmeN0qd+y0jszEtoY48r0Peq5dwMEkIlCOu6Q5f41lfkswXuKtYrhgoTpLnyIcHm24Uhqx+5Tqm2InSwLhE6Q=="
+          "integrity": "sha512-ojmeN0qd+y0jszEtoY48r0Peq5dwMEkIlCOu6Q5f41lfkswXuKtYrhgoTpLnyIcHm24Uhqx+5Tqm2InSwLhE6Q==",
+          "dev": true
         },
         "shebang-command": {
           "version": "2.0.0",
           "resolved": "https://registry.npmjs.org/shebang-command/-/shebang-command-2.0.0.tgz",
           "integrity": "sha512-kHxr2zZpYtdmrN1qDjrrX/Z1rR1kG8Dx+gkpK1G4eXmvXswmcE1hTWBWYUzlraYw1/yZp6YuDY77YtvbN0dmDA==",
+          "dev": true,
           "requires": {
             "shebang-regex": "^3.0.0"
           }
@@ -7802,12 +7811,14 @@
         "shebang-regex": {
           "version": "3.0.0",
           "resolved": "https://registry.npmjs.org/shebang-regex/-/shebang-regex-3.0.0.tgz",
-          "integrity": "sha512-7++dFhtcx3353uBaq8DDR4NuxBetBzC7ZQOhmTQInHEd6bSrXdiEyzCvG07Z44UYdLShWUyXt5M/yhz8ekcb1A=="
+          "integrity": "sha512-7++dFhtcx3353uBaq8DDR4NuxBetBzC7ZQOhmTQInHEd6bSrXdiEyzCvG07Z44UYdLShWUyXt5M/yhz8ekcb1A==",
+          "dev": true
         },
         "which": {
           "version": "2.0.2",
           "resolved": "https://registry.npmjs.org/which/-/which-2.0.2.tgz",
           "integrity": "sha512-BLI3Tl1TW3Pvl70l3yq3Y64i+awpwXqsGBYWkkqMtnbXgrMD+yj7rhW0kuEDxzJaYXGjEW5ogapKNMEKNMjibA==",
+          "dev": true,
           "requires": {
             "isexe": "^2.0.0"
           }
@@ -8579,7 +8590,8 @@
     "isexe": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/isexe/-/isexe-2.0.0.tgz",
-      "integrity": "sha1-6PvzdNxVb/iUehDcsFctYz8s+hA="
+      "integrity": "sha1-6PvzdNxVb/iUehDcsFctYz8s+hA=",
+      "dev": true
     },
     "istanbul-lib-coverage": {
       "version": "3.2.0",
diff --git a/src/utils.js b/src/utils.js
index e4ab49c..51e1000 100644
--- a/src/utils.js
+++ b/src/utils.js
@@ -624,7 +624,11 @@ const utils = {
         c = p[2],
         d = a - 2 * b + c;
       if (d !== 0) {
-        const m1 = -sqrt(b * b - a * c),
+        const m1Pow2 = b * b - a * c;
+        if (m1Pow2 < 0) {
+          return [];
+        }
+        const m1 = -sqrt(m1Pow2),
           m2 = -a + b,
           v1 = -(m1 + m2) / d,
           v2 = -(-m1 + m2) / d;