diff --git a/article.js b/article.js index 5c85062f..c97a751a 100644 --- a/article.js +++ b/article.js @@ -62,7 +62,7 @@ var React = __webpack_require__(8); var ReactDOM = __webpack_require__(165); var Article = __webpack_require__(166); - var style = __webpack_require__(185); + var style = __webpack_require__(183); ReactDOM.render(React.createElement(Article, null), document.getElementById("article")); @@ -19751,10 +19751,10 @@ preface: __webpack_require__(168), introduction: __webpack_require__(169), whatis: __webpack_require__(176), - explanation: __webpack_require__(180), - control: __webpack_require__(182), - matrix: __webpack_require__(183), - decasteljau: __webpack_require__(184) + explanation: __webpack_require__(178), + control: __webpack_require__(180), + matrix: __webpack_require__(181), + decasteljau: __webpack_require__(182) }; /* @@ -24079,7 +24079,6 @@ var React = __webpack_require__(8); var Graphic = __webpack_require__(170); var SectionHeader = __webpack_require__(175); - var LaTeX = __webpack_require__(177); var Whatis = React.createClass({ displayName: "Whatis", @@ -24088,7 +24087,7 @@ title: "So what makes a Bézier Curve?" }, - interpolation: __webpack_require__(179), + interpolation: __webpack_require__(177), componentWillMount: function componentWillMount() { this.setup = this.interpolation.setup.bind(this); @@ -24132,7 +24131,7 @@ "If we know the distance between those two points, and we want a new point that is, say, 20% the distance away from the first point (and thus 80% the distance away from the second point) then we can compute that really easily:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/93b03244097aea8be8fcac493afd3706c79fa403.svg" }) ), @@ -24165,47 +24164,6 @@ /***/ }, /* 177 */ -/***/ function(module, exports, __webpack_require__) { - - "use strict"; - - var React = __webpack_require__(8); - var ReactDOM = __webpack_require__(165); - var noop = __webpack_require__(178); - - var MathJax = typeof window !== "undefined" ? window.MathJax : false; - - // fallback will simply do nothing when typesetting. - if (!MathJax) { - MathJax = { Hub: { Queue: noop } }; - } - - var LaTeX = React.createClass({ - displayName: "LaTeX", - - render: function render() { - return React.createElement( - "p", - { ref: "latex" }, - this.props.children - ); - } - }); - - module.exports = LaTeX; - -/***/ }, -/* 178 */ -/***/ function(module, exports) { - - /** - * because somethings you just need a no-op - */ - module.exports = function noop() {}; - - -/***/ }, -/* 179 */ /***/ function(module, exports) { "use strict"; @@ -24371,7 +24329,7 @@ }; /***/ }, -/* 180 */ +/* 178 */ /***/ function(module, exports, __webpack_require__) { "use strict"; @@ -24379,7 +24337,6 @@ var React = __webpack_require__(8); var Graphic = __webpack_require__(170); var SectionHeader = __webpack_require__(175); - var LaTeX = __webpack_require__(177); var Explanation = React.createClass({ displayName: "Explanation", @@ -24388,7 +24345,7 @@ title: "The basics of Bézier curves" }, - circle: __webpack_require__(181), + circle: __webpack_require__(179), componentWillMount: function componentWillMount() { this.setup = this.circle.setup.bind(this); @@ -24422,7 +24379,7 @@ ", to some other value, using some kind of number manipulation:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/1702a1f7b6c180a18d2e94b25808262b1e4c6195.svg" }) ), @@ -24467,7 +24424,7 @@ "So far so good. Now, let's look at parametric functions, and how they cheat. Let's take the following two functions:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/90842920b7553c3091917cfc38fc0a67c2055d38.svg" }) ), @@ -24495,7 +24452,7 @@ " isn't used in that function. Parametric functions cheat by changing that. In a parametric function all the different functions share a variable, like this:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/e5fb9f01d6545e3e2f43410625edfdf483eb3668.svg" }) ), @@ -24559,7 +24516,7 @@ " with what we usually mean with them for parametric curves, things might be a lot more obvious:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/a1189e16ce64ad24e90aa3ea75a724f05d7ab599.svg" }) ), @@ -24687,7 +24644,7 @@ "You may remember polynomials from high school, where they're those sums that look like:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/4f7c9e4f8c7c560ba061ebd09e8a63364401ff22.svg" }) ), @@ -24756,7 +24713,7 @@ " etc. taking the \"binomial\" form, which sounds fancy but is actually a pretty simple description for mixing values:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/0d76eda1bc302fcbae9ad77311288ffb9935e9f0.svg" }) ), @@ -24772,7 +24729,7 @@ " and add in \"times one\", things suddenly look pretty easy. Check out these binomial terms:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/b7307b83a6aed8f3981842ce4365cddaaad5ba3b.svg" }) ), @@ -24817,7 +24774,7 @@ ", and remove the weights for a moment, we get this:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/85716f7b80fabb43411b982ea3c2919f01f546b6.svg" }) ), @@ -24851,7 +24808,7 @@ "'s after every + sign. So that's actually pretty simple too. So now you know binomial polynomials, and just for completeness I'm going to show you the generic function for this:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/524d2b97aebbfe44de7529989629e4e0dd11a754.svg" }) ), @@ -25009,7 +24966,7 @@ module.exports = Explanation; /***/ }, -/* 181 */ +/* 179 */ /***/ function(module, exports) { "use strict"; @@ -25051,7 +25008,7 @@ }; /***/ }, -/* 182 */ +/* 180 */ /***/ function(module, exports, __webpack_require__) { "use strict"; @@ -25059,7 +25016,6 @@ var React = __webpack_require__(8); var Graphic = __webpack_require__(170); var SectionHeader = __webpack_require__(175); - var LaTeX = __webpack_require__(177); var Control = React.createClass({ displayName: "Control", @@ -25291,7 +25247,7 @@ "If we want to change the curve, we need to change the weights of each point, effectively changing the interpolations. The way to do this is about as straight forward as possible: just multiply each point with a value that changes its strength. These values are conventionally called \"Weights\", and we can add them to our original Bézier function:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/e41083ef7693be5384f724a8b354b5a38c9b0ed4.svg" }) ), @@ -25324,7 +25280,7 @@ " is our last coordinate, and everything in between is a controlling coordinate. Say we want a cubic curve that starts at (120,160), is controlled by (35,200) and (220,260) and ends at (220,40), we use this Bézier curve:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/13a1df3fc05f3610035843aee9ee6be82a5820e7.svg" }) ), @@ -25440,14 +25396,13 @@ **/ /***/ }, -/* 183 */ +/* 181 */ /***/ function(module, exports, __webpack_require__) { "use strict"; var React = __webpack_require__(8); var SectionHeader = __webpack_require__(175); - var LaTeX = __webpack_require__(177); var Matrix = React.createClass({ displayName: "Matrix", @@ -25471,7 +25426,7 @@ "We can also represent Bézier as matrix operations, by expressing the Bézier formula as a polynomial basis function, the weight matrix, and the actual coordinates as matrix. Let's look at what this means for the cubic curve :" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/27810102a13621b9a1e3a533516ffec96f98694a.svg" }) ), @@ -25481,7 +25436,7 @@ "Disregarding our actual coordinates for a moment, we have:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/57e8df56566add302c750691d8f83ee0863ca888.svg" }) ), @@ -25491,7 +25446,7 @@ "We can write this as a sum of four expressions:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/db3823d8088bd7efa7af9fc9f0db34580a364e22.svg" }) ), @@ -25501,7 +25456,7 @@ "And we can expand these expressions:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/7917f77b496627b3f54b0678ee5e253c7773fd8b.svg" }) ), @@ -25511,7 +25466,7 @@ "Furthermore, we can make all the 1 and 0 factors explicit:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/73e32c4b471bc1751add68148d9acababcf43ff1.svg" }) ), @@ -25527,7 +25482,7 @@ ", we can view as a series of four matrix operations:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/98f76abba92e71685cc2d94f0a9f482b6cbe554e.svg" }) ), @@ -25537,7 +25492,7 @@ "If we compact this into a single matrix operation, we get:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/e4496d76627a594150c9034f6c011bcb1cfe853c.svg" }) ), @@ -25553,7 +25508,7 @@ " matrix horizontally, and our big \"mixing\" matrix upside down:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/bbfe6ae9683fb2be29df8db065e1004b94066780.svg" }) ), @@ -25563,7 +25518,7 @@ "And then finally, we can add in our original coordinates as a single third matrix:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/6f51af1c66ef77785066ea5601e7dc5064831401.svg" }) ), @@ -25573,7 +25528,7 @@ "We can perform the same trick for the quadratic curve, in which case we end up with:" ), React.createElement( - LaTeX, + "p", null, React.createElement("img", { className: "LaTeX SVG", src: "images/latex/8fa7f5a1b32d06d66b0a4d0f000b2496e0bacccd.svg" }) ), @@ -25622,7 +25577,7 @@ module.exports = Matrix; /***/ }, -/* 184 */ +/* 182 */ /***/ function(module, exports, __webpack_require__) { "use strict"; @@ -25630,7 +25585,6 @@ var React = __webpack_require__(8); var Graphic = __webpack_require__(170); var SectionHeader = __webpack_require__(175); - var LaTeX = __webpack_require__(177); var deCasteljau = React.createClass({ displayName: "deCasteljau", @@ -25937,16 +25891,16 @@ module.exports = deCasteljau; /***/ }, -/* 185 */ +/* 183 */ /***/ function(module, exports, __webpack_require__) { // style-loader: Adds some css to the DOM by adding a