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2d-matrix.html
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<html>
<title>2D matrix transformations</title>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.10.1/jquery.min.js"></script>
<script src="js/SVGBuilder.js" charset="utf-8"></script>
<script src="js/Matrix.js" charset="utf-8"></script>
<script src="js/Vertex.js" charset="utf-8"></script>
<script>
function Plot2D(containerId) {
this.containerId = containerId;
this.shapes = {};
}
Plot2D.prototype.addShape = function(shapeId, shape) {
this.shapes[shapeId] = shape;
}
Plot2D.prototype.update = function(extraContent) {
var svgContent = new SVGBuilder();
var container = document.getElementById(this.containerId);
var viewboxWidth = container.offsetWidth;
var viewboxHeight = container.offsetHeight;
this.origin = {x:viewboxWidth / 2, y:viewboxHeight / 2};
// Draw the axis and gridlines
for (var x = this.origin.x - 10 * Math.round(this.origin.x / 10); x < viewboxWidth; x += 10) {
svgContent.addLine({
"x1": x,
"y1": 0,
"x2": x,
"y2": viewboxHeight,
"class": "systemGridLine"
});
}
for (var y = this.origin.y - 10 * Math.round(this.origin.y / 10); y < viewboxHeight; y += 10) {
svgContent.addLine({
"x1": 0,
"y1": y,
"x2": viewboxWidth,
"y2": y,
"class": "systemGridLine"
});
}
svgContent.addLine({
"x1": this.origin.x,
"y1": 0,
"x2": this.origin.x,
"y2": viewboxHeight,
"class": "systemAxisLine"
});
svgContent.addLine({
"x1": 0,
"y1": this.origin.y,
"x2": viewboxWidth,
"y2": this.origin.y,
"class": "systemAxisLine"
});
// Draw the shapes
for (var shapeId in this.shapes) {
var shape = this.shapes[shapeId];
shape.xform();
for (var pi = 0, shapeStart = null; pi <= shape.xdata.length; pi++) {
if (shapeStart === null) {
shapeStart = pi;
continue;
}
if (pi == shape.xdata.length || shape.xdata[pi] === null) {
if (shape.type == "closed") {
// End of current piece, so close the end
svgContent.addLine({
"x1": this.origin.x + shape.xdata[pi - 1].x,
"y1": this.origin.y + shape.xdata[pi - 1].y,
"x2": this.origin.x + shape.xdata[shapeStart].x,
"y2": this.origin.y + shape.xdata[shapeStart].y,
"class": shape["class"]
});
}
shapeStart = null;
} else {
svgContent.addLine({
"x1": this.origin.x + shape.xdata[pi - 1].x,
"y1": this.origin.y + shape.xdata[pi - 1].y,
"x2": this.origin.x + shape.xdata[pi].x,
"y2": this.origin.y + shape.xdata[pi].y,
"class": shape["class"]
});
}
}
}
if (extraContent) {
extraContent(this, svgContent);
}
svgContent.insert(container, true);
}
function Plot2DShape(data, type, shapeClass) {
this.data = data;
this.type = type;
this["class"] = shapeClass;
this.matrix = null;
this.xdata = []; // Stores data with transformed vertexes
this.xform();
}
Plot2DShape.prototype.xform = function(matrix) {
if (matrix) this.matrix = matrix;
for (var pi = 0; pi < this.data.length; pi++) {
if (this.data[pi] !== null) {
var v = new Vertex2D(this.data[pi].x, this.data[pi].y);
if (this.matrix) {
var m = this.matrix;
v = v.xform(new Matrix(2, 2, [
m.xx, m.xy,
m.yx, m.yy
]));
v = v.translate(
m.xt,
m.yt
);
}
this.xdata[pi] = v;
} else {
this.xdata[pi] = null;
}
}
}
Plot2DShape.prototype.testInside = function(pt) {
// Tests if the point is inside the shape
// Reference: http://jsfromhell.com/math/is-point-in-poly and https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.html
if (this.type != "closed") return false;
// Prepare the dataset in correct format to handle multiple pieces/holes
var poly = [];
poly.push({x:0, y:0});
for (var pi = 0, shapeStart = null; pi <= this.xdata.length; pi++) {
if (shapeStart === null) {
shapeStart = pi;
}
if (pi == this.xdata.length || this.xdata[pi] === null) {
poly.push(this.xdata[shapeStart]);
poly.push({x:0, y:0});
shapeStart = null;
} else {
poly.push(this.xdata[pi]);
}
}
// Do the test
for(var c = false, i = -1, l = poly.length, j = l - 1; ++i < l; j = i)
((poly[i].y <= pt.y && pt.y < poly[j].y) || (poly[j].y <= pt.y && pt.y < poly[i].y))
&& (pt.x < (poly[j].x - poly[i].x) * (pt.y - poly[i].y) / (poly[j].y - poly[i].y) + poly[i].x)
&& (c = !c);
return c;
}
Plot2DShape.text2data = function(text) {
var lines = text.split(/\n/g);
var output = [];
var status = true;
lines.forEach(function(line) {
if (!line.trim()) {
if (!output.length || output[output.length - 1] !== null) output.push(null);
return;
}
var values = /^(-?\d*\.?\d*)\s*(-?\d*\.?\d*)/.exec(line);
if (values) {
var v = {
x: parseFloat(values[1]),
y: parseFloat(values[2])
};
if (isNaN(v.x) || isNaN(v.y)) {
status = false;
} else {
output.push(v);
}
} else {
status = false;
}
});
// Strip the leading nulls
while (output.length && output[0] === null) output.shift();
// Strip the trailing nulls
while (output.length && output[output.length - 1] === null) output.pop();
return status ? output : null;
}
$(function() {
var plot = new Plot2D("graphics");
/*
var shapeData_A = [
{x: 40, y: 0},
{x: 70, y: 0},
{x:110, y:120},
{x: 80, y:120},
{x: 70, y: 90},
{x: 40, y: 90},
{x: 30, y:120},
{x: 0, y:120},
null,
{x: 50, y: 60},
{x: 55, y: 45},
{x: 60, y: 60}
];
plot.addShape("A", new Plot2DShape(shapeData_A, "closed", "polyLineGreen"));
plot.addShape("A1", new Plot2DShape(shapeData_A, "closed", "polyLineRed"));
*/
plot.update();
var DragMaster = {
activeHandler: null,
dragStart: null,
registerHandler: function(handler) {
$("#" + handler.dragHandleId).bind("mousedown", function(event) {
DragMaster.activeHandler = handler;
handler.onstart();
DragMaster.dragStart = {
x: event.pageX,
y: event.pageY
}
event.preventDefault();
});
},
init: function() {
$(window).bind("mousemove", function(event) {
if (DragMaster.activeHandler) {
var dragVector = {
x: event.pageX - DragMaster.dragStart.x,
y: event.pageY - DragMaster.dragStart.y
};
DragMaster.activeHandler.ondrag(dragVector);
}
});
$(window).bind("mouseup", function(event) {
if (DragMaster.activeHandler) {
DragMaster.activeHandler.onend();
DragMaster.activeHandler = null;
}
});
}
}
// Matrix value input drag handlers
function MatrixValue(id) {
this.id = id;
this.dragHandleId = "matrix-" + id + "-handle";
this.ctr = document.getElementById("matrix-" + id);
this.startValue = null;
this.step = MatrixValue.step[id];
var self = this;
// Populate the default value
this.ctr.value = MatrixValue.matrix[id];
// Bind the change event
$(this.ctr).bind("change", function(event) {
MatrixValue.matrix[id] = parseFloat(event.target.value);
self.updatePlot();
});
}
MatrixValue.matrix = {
xx: 1, xy: 0, xt: 0,
yx: 0, yy: 1, yt: 0
};
MatrixValue.step = {
xx: 0.1, xy: 0.1, xt: 1,
yx: 0.1, yy: 0.1, yt: 1
};
MatrixValue.prototype.onstart = function() {
// Invoked when user presses mouse button
this.startValue = parseFloat(this.ctr.value);
}
MatrixValue.prototype.ondrag = function(dragVector) {
// Invoked when user drags mouse
var newValue = this.startValue + this.step * (dragVector.x + dragVector.y);
MatrixValue.matrix[this.id] = newValue;
this.ctr.value = Math.round(1000 * newValue) / 1000;
this.updatePlot();
}
MatrixValue.prototype.onend = function(id) {
// Invoked when user releases the mouse button
}
MatrixValue.prototype.updatePlot = function() {
plot.update();
}
// Register the drag handlers
for (var matrixValueId in MatrixValue.matrix) {
DragMaster.registerHandler(new MatrixValue(matrixValueId));
}
DragMaster.init();
$("#hitTest").bind("click", function(event) {
plot.update(function(plot, svgContent) {
for (var x = -400; x <= 400; x += 10) {
for (var y = -300; y <= 300; y += 10) {
if (plot.shapes.A1.testInside({x:x + 5, y:y + 5})) {
svgContent.addRect({
"x": plot.origin.x + x + 1,
"y": plot.origin.y + y + 1,
"width": 9,
"height": 9,
"class": "hitTest"
});
}
}
}
})
});
var defaultShapeData = [
"40 0",
"70 0",
"110 120",
"80 120",
"70 90",
"40 90",
"30 120",
"0 120",
"",
"50 60",
"55 45",
"60 60"
].join("\n");
$("#shapeData").bind("input", function(event) {
var shapeData = Plot2DShape.text2data(event.target.value);
if (shapeData) {
$(event.target).css("background-color","#fff");
plot.shapes = {};
plot.addShape("A", new Plot2DShape(shapeData, "closed", "polyLineGreen"));
plot.addShape("A1", new Plot2DShape(shapeData, "closed", "polyLineRed"));
// Link the matrix
plot.shapes["A1"].matrix = MatrixValue.matrix;
plot.update();
} else {
$(event.target).css("background-color","#fee");
}
});
$("#shapeData").val(defaultShapeData);
$("#shapeData").trigger("input");
});
</script>
<style type="text/css">
#testbox {
position:absolute;
left:30px;
top:30px;
width:800px;
height:600px;
text-align:center;
cursor: crosshair;
-moz-user-select: none; -webkit-user-select: none; -ms-user-select:none; user-select:none;-o-user-select:none;
border: 1px solid #eee;
background-color:#fff;
}
#graphics {
position: absolute;
width: 100%;
height: 100%;
top: 0px;
left: 0px;
}
#graphics svg {
width: 100%;
height: 100%;
}
#inputPanel {
position:absolute;
left:840px;
top:30px;
width:250px;
height:600px;
padding: 10px;
text-align:center;
border: 1px solid #eee;
background-color:#fff;
}
#inputPanel h1 {
clear: both;
font-size: 20px;
font-family: sans-serif, Arial;
font-weight: bold;
}
#inputPanel input.matrix-value {
float: left;
width: 50px;
}
#inputPanel span.dragHandle {
width: 16px;
height: 16px;
background: #ccc;
display: block;
margin: 2px 10px 2px 2px;
float: left;
border-radius: 50%;
cursor: row-resize;
}
.systemAxisLine {
stroke: #8888;
stroke-width: 2;
}
.systemGridLine {
stroke: #eee;
stroke-width: 1;
}
.polyLineGreen {
stroke: #0e0;
stroke-width: 2;
}
.polyLineRed {
stroke: #e00;
stroke-width: 1.5;
}
.hitTest {
fill: #00f;
}
</style>
<body>
<div id="testbox">
<div id="graphics"></div>
</div>
<div id="inputPanel">
<h1>Shape data</h1>
<textarea id="shapeData" style="width:100%; height:200px;"></textarea>
<h1>Transformation matrix</h1>
<input id= "matrix-xx" type="text" class="matrix-value"><span id="matrix-xx-handle" class="dragHandle"></span>
<input id= "matrix-xy" type="text" class="matrix-value"><span id="matrix-xy-handle" class="dragHandle"></span>
<input id= "matrix-xt" type="text" class="matrix-value"><span id="matrix-xt-handle" class="dragHandle"></span>
<br>
<input id= "matrix-yx" type="text" class="matrix-value"><span id="matrix-yx-handle" class="dragHandle"></span>
<input id= "matrix-yy" type="text" class="matrix-value"><span id="matrix-yy-handle" class="dragHandle"></span>
<input id= "matrix-yt" type="text" class="matrix-value"><span id="matrix-yt-handle" class="dragHandle"></span>
<h1>Hit test</h1>
<button id="hitTest">Test</button>
</div>
</body>
</html>