The cyan grid is positioned manually in JavaScript by apply a matrix transformation. The underlying magenta grid is positioned with a CSS matrix3d transform, and should exactly align with the cyan grid.
On Firefox on a Retina (HiDPI), the magenta grid does not correctly align with the cyan grid. On Chrome, Safari and Firefox when the page is zoomed, the magenta grid does not correctly align with the cyan grid.
| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| body { | |
| position: relative; | |
| } | |
| svg { | |
| position: absolute; | |
| top: 0; | |
| left: 0; | |
| } | |
| .handle { | |
| stroke: #fff; | |
| stroke-width: 2px; | |
| } | |
| .line { | |
| stroke-width: 1.5px; | |
| stroke-linecap: square; | |
| } | |
| #expected .line { | |
| stroke: cyan; | |
| } | |
| #actual .line { | |
| stroke: magenta; | |
| } | |
| </style> | |
| <body> | |
| <script src="//d3js.org/d3.v3.min.js"></script> | |
| <script src="numeric-solve.min.js"></script> | |
| <script> | |
| var margin = {top: 50, right: 280, bottom: 50, left: 280}, | |
| width = 960, | |
| height = 500; | |
| var transform = ["", "-webkit-", "-moz-", "-ms-", "-o-"].reduce(function(p, v) { return v + "transform" in document.body.style ? v : p; }) + "transform"; | |
| var sourcePoints = [[0, 0], [960, 0], [960, 500], [0, 500]], | |
| targetPoints = [[280, 50], [688, 33], [680, 450], [341, 371]]; | |
| var svg = d3.select("body").selectAll("svg") | |
| .data(["actual", "expected"]) | |
| .enter().append("svg") | |
| .attr("id", function(d) { return d; }) | |
| .attr("width", width) | |
| .attr("height", height); | |
| svg.selectAll(".line") | |
| .data(d3.range(0, width + 1, width / 10).map(function(x) { return [[x, 0], [x, height]]; }) | |
| .concat(d3.range(0, height + 1, height / 10).map(function(y) { return [[0, y], [width, y]]; }))) | |
| .enter().append("path") | |
| .attr("class", "line") | |
| .attr("d", function(d) { return "M" + d[0] + "L" + d[1]; }); | |
| var svgActual = d3.select("#actual") | |
| .style(transform + "-origin", "0px 0px 0"); | |
| var svgExpected = d3.select("#expected"); | |
| svgExpected.selectAll(".handle") | |
| .data(targetPoints) | |
| .enter().append("circle") | |
| .attr("class", "handle") | |
| .attr("transform", function(d) { return "translate(" + d + ")"; }) | |
| .attr("r", 7) | |
| .call(d3.behavior.drag() | |
| .origin(function(d) { return {x: d[0], y: d[1]}; }) | |
| .on("drag", dragged)); | |
| var lineExpected = svgExpected.selectAll(".line"); | |
| transformed(); | |
| function dragged(d) { | |
| d3.select(this).attr("transform", "translate(" + (d[0] = d3.event.x) + "," + (d[1] = d3.event.y) + ")"); | |
| transformed(); | |
| } | |
| function transformed() { | |
| for (var a = [], b = [], i = 0, n = sourcePoints.length; i < n; ++i) { | |
| var s = sourcePoints[i], t = targetPoints[i]; | |
| a.push([s[0], s[1], 1, 0, 0, 0, -s[0] * t[0], -s[1] * t[0]]), b.push(t[0]); | |
| a.push([0, 0, 0, s[0], s[1], 1, -s[0] * t[1], -s[1] * t[1]]), b.push(t[1]); | |
| } | |
| var X = solve(a, b, true), matrix = [ | |
| X[0], X[3], 0, X[6], | |
| X[1], X[4], 0, X[7], | |
| 0, 0, 1, 0, | |
| X[2], X[5], 0, 1 | |
| ].map(function(x) { | |
| return d3.round(x, 6); | |
| }); | |
| svgActual.style(transform, "matrix3d(" + matrix + ")"); | |
| lineExpected.attr("d", function(d) { return "M" + project(matrix, d[0]) + "L" + project(matrix, d[1]); }); | |
| } | |
| // Given a 4x4 perspective transformation matrix, and a 2D point (a 2x1 vector), | |
| // applies the transformation matrix by converting the point to homogeneous | |
| // coordinates at z=0, post-multiplying, and then applying a perspective divide. | |
| function project(matrix, point) { | |
| point = multiply(matrix, [point[0], point[1], 0, 1]); | |
| return [point[0] / point[3], point[1] / point[3]]; | |
| } | |
| // Post-multiply a 4x4 matrix in column-major order by a 4x1 column vector: | |
| // [ m0 m4 m8 m12 ] [ v0 ] [ x ] | |
| // [ m1 m5 m9 m13 ] * [ v1 ] = [ y ] | |
| // [ m2 m6 m10 m14 ] [ v2 ] [ z ] | |
| // [ m3 m7 m11 m15 ] [ v3 ] [ w ] | |
| function multiply(matrix, vector) { | |
| return [ | |
| matrix[0] * vector[0] + matrix[4] * vector[1] + matrix[8 ] * vector[2] + matrix[12] * vector[3], | |
| matrix[1] * vector[0] + matrix[5] * vector[1] + matrix[9 ] * vector[2] + matrix[13] * vector[3], | |
| matrix[2] * vector[0] + matrix[6] * vector[1] + matrix[10] * vector[2] + matrix[14] * vector[3], | |
| matrix[3] * vector[0] + matrix[7] * vector[1] + matrix[11] * vector[2] + matrix[15] * vector[3] | |
| ]; | |
| } | |
| </script> |
| GENERATED_FILES = \ | |
| numeric-solve.min.js | |
| all: $(GENERATED_FILES) | |
| clean: | |
| rm -rf -- $(GENERATED_FILES) build | |
| numeric-solve.min.js: numeric-solve.js | |
| node_modules/.bin/uglifyjs numeric-solve.js -c -m -o $@ |
| numeric.js | |
| Copyright (C) 2011 by Sébastien Loisel | |
| Permission is hereby granted, free of charge, to any person obtaining a copy of | |
| this software and associated documentation files (the "Software"), to deal in | |
| the Software without restriction, including without limitation the rights to | |
| use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of | |
| the Software, and to permit persons to whom the Software is furnished to do so, | |
| subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in all | |
| copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS | |
| FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR | |
| COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER | |
| IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN | |
| CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
| (function() { | |
| var abs = Math.abs; | |
| function _foreach2(x, s, k, f) { | |
| if (k === s.length - 1) return f(x); | |
| var i, n = s[k], ret = Array(n); | |
| for (i = n - 1; i >= 0; --i) ret[i] = _foreach2(x[i], s, k + 1, f); | |
| return ret; | |
| } | |
| function _dim(x) { | |
| var ret = []; | |
| while (typeof x === "object") ret.push(x.length), x = x[0]; | |
| return ret; | |
| } | |
| function dim(x) { | |
| var y, z; | |
| if (typeof x === "object") { | |
| y = x[0]; | |
| if (typeof y === "object") { | |
| z = y[0]; | |
| if (typeof z === "object") { | |
| return _dim(x); | |
| } | |
| return [x.length, y.length]; | |
| } | |
| return [x.length]; | |
| } | |
| return []; | |
| } | |
| function cloneV(x) { | |
| var _n = x.length, i, ret = Array(_n); | |
| for (i = _n - 1; i !== -1; --i) ret[i] = x[i]; | |
| return ret; | |
| } | |
| function clone(x) { | |
| return typeof x !== "object" ? x : _foreach2(x, dim(x), 0, cloneV); | |
| } | |
| function LU(A, fast) { | |
| fast = fast || false; | |
| var i, j, k, absAjk, Akk, Ak, Pk, Ai, | |
| max, | |
| n = A.length, n1 = n - 1, | |
| P = new Array(n); | |
| if (!fast) A = clone(A); | |
| for (k = 0; k < n; ++k) { | |
| Pk = k; | |
| Ak = A[k]; | |
| max = abs(Ak[k]); | |
| for (j = k + 1; j < n; ++j) { | |
| absAjk = abs(A[j][k]); | |
| if (max < absAjk) { | |
| max = absAjk; | |
| Pk = j; | |
| } | |
| } | |
| P[k] = Pk; | |
| if (Pk != k) { | |
| A[k] = A[Pk]; | |
| A[Pk] = Ak; | |
| Ak = A[k]; | |
| } | |
| Akk = Ak[k]; | |
| for (i = k + 1; i < n; ++i) { | |
| A[i][k] /= Akk; | |
| } | |
| for (i = k + 1; i < n; ++i) { | |
| Ai = A[i]; | |
| for (j = k + 1; j < n1; ++j) { | |
| Ai[j] -= Ai[k] * Ak[j]; | |
| ++j; | |
| Ai[j] -= Ai[k] * Ak[j]; | |
| } | |
| if (j===n1) Ai[j] -= Ai[k] * Ak[j]; | |
| } | |
| } | |
| return { | |
| LU: A, | |
| P: P | |
| }; | |
| } | |
| function LUsolve(LUP, b) { | |
| var i, j, | |
| LU = LUP.LU, | |
| n = LU.length, | |
| x = clone(b), | |
| P = LUP.P, | |
| Pi, LUi, tmp; | |
| for (i = n - 1; i !== -1; --i) x[i] = b[i]; | |
| for (i = 0; i < n; ++i) { | |
| Pi = P[i]; | |
| if (P[i] !== i) tmp = x[i], x[i] = x[Pi], x[Pi] = tmp; | |
| LUi = LU[i]; | |
| for (j = 0; j < i; ++j) { | |
| x[i] -= x[j] * LUi[j]; | |
| } | |
| } | |
| for (i = n - 1; i >= 0; --i) { | |
| LUi = LU[i]; | |
| for (j = i + 1; j < n; ++j) { | |
| x[i] -= x[j] * LUi[j]; | |
| } | |
| x[i] /= LUi[i]; | |
| } | |
| return x; | |
| } | |
| solve = function(A, b, fast) { | |
| return LUsolve(LU(A, fast), b); | |
| }; | |
| })(); |
| !function(){function r(t,n,o,e){if(o===n.length-1)return e(t);var f,u=n[o],c=Array(u);for(f=u-1;f>=0;--f)c[f]=r(t[f],n,o+1,e);return c}function t(r){for(var t=[];"object"==typeof r;)t.push(r.length),r=r[0];return t}function n(r){var n,o;return"object"==typeof r?(n=r[0],"object"==typeof n?(o=n[0],"object"==typeof o?t(r):[r.length,n.length]):[r.length]):[]}function o(r){var t,n=r.length,o=Array(n);for(t=n-1;-1!==t;--t)o[t]=r[t];return o}function e(t){return"object"!=typeof t?t:r(t,n(t),0,o)}function f(r,t){t=t||!1;var n,o,f,u,a,h,i,l,g,v=r.length,y=v-1,b=new Array(v);for(t||(r=e(r)),f=0;v>f;++f){for(i=f,h=r[f],g=c(h[f]),o=f+1;v>o;++o)u=c(r[o][f]),u>g&&(g=u,i=o);for(b[f]=i,i!=f&&(r[f]=r[i],r[i]=h,h=r[f]),a=h[f],n=f+1;v>n;++n)r[n][f]/=a;for(n=f+1;v>n;++n){for(l=r[n],o=f+1;y>o;++o)l[o]-=l[f]*h[o],++o,l[o]-=l[f]*h[o];o===y&&(l[o]-=l[f]*h[o])}}return{LU:r,P:b}}function u(r,t){var n,o,f,u,c,a=r.LU,h=a.length,i=e(t),l=r.P;for(n=h-1;-1!==n;--n)i[n]=t[n];for(n=0;h>n;++n)for(f=l[n],l[n]!==n&&(c=i[n],i[n]=i[f],i[f]=c),u=a[n],o=0;n>o;++o)i[n]-=i[o]*u[o];for(n=h-1;n>=0;--n){for(u=a[n],o=n+1;h>o;++o)i[n]-=i[o]*u[o];i[n]/=u[n]}return i}var c=Math.abs;solve=function(r,t,n){return u(f(r,n),t)}}(); |
| { | |
| "name": "anonymous", | |
| "version": "0.0.1", | |
| "private": true, | |
| "dependencies": { | |
| "uglify-js": "2" | |
| } | |
| } |
