我使用帆布3D绘制三维图，其中我可以绘制点，例如（1,5,4），（-8,6，-2）etc.So我能够在所有正和负x绘制， y和z axis.I也有通过使用箭头键旋转效果。 旋转操作的指令：z轴从屏幕的中心延伸出来。
绕X轴，按上/下箭头键。 绕Y轴，按左/右箭头键。 绕z轴，按下Ctrl +左/ CTRL +向下箭头键。
我可以通过我提供的文本字段指定点绘制点。 现在的问题是，例如，如果我图（5,5,2），它会绘制properly.But如果我旋转x轴的第一和则y轴则指向将被适当地作图。 问题就来了，如果我旋转y轴的第一和然后X-axis.the点将被错误地作图。 找到我所遇到的问题，简单的方法：这可以很容易找到，如果你去上绘制的相同点repeatedly.The点应相同点之上绘制，以便只有单点visible.But在我的案件的相同点（为EX（5,5,2）是在画布上不同的地方拉，而rotating.This问题只说到，如果我先旋转y轴，然后X轴还是我先旋转Z轴，然后Y轴。那么是什么是我在做coding.I错误是新来这个帆布3D和java script.So请帮助。
<html>
<head>
<script src="http://code.jquery.com/jquery-latest.min.js"></script>
<title>Canvas Surface Rotation</title>
<style>
body {
text-align: center;
}
canvas {
border: 1px solid black;
}
</style>
<script>
var p1;
var p2;
var p3;
var p4;
var p5;
var p6;
var xangle=0;
var yangle=0;
var zangle=0;
var constants = {
canvasWidth: 600, // In pixels.
canvasHeight: 600, // In pixels.
leftArrow: 37,
upArrow: 38,
rightArrow: 39,
downArrow: 40,
xMin: -10, // These four max/min values define a square on the xy-plane that the surface will be plotted over.
xMax: 10,
yMin: -10,
yMax: 10,
xDelta: 0.06, // Make smaller for more surface points.
yDelta: 0.06, // Make smaller for more surface points.
colorMap: ["#000080"], // There are eleven possible "vertical" color values for the surface, based on the last row of http://www.cs.siena.edu/~lederman/truck/AdvanceDesignTrucks/html_color_chart.gif
pointWidth: 2, // The size of a rendered surface point (i.e., rectangle width and height) in pixels.
dTheta: 0.05, // The angle delta, in radians, by which to rotate the surface per key press.
surfaceScale: 24 // An empirically derived constant that makes the surface a good size for the given canvas size.
};
// These are constants too but I've removed them from the above constants literal to ease typing and improve clarity.
var X = 0;
var Y = 1;
var Z = 2;
// -----------------------------------------------------------------------------------------------------
var controlKeyPressed = false; // Shared between processKeyDown() and processKeyUp().
var surface = new Surface(); // A set of points (in vector format) representing the surface.
// -----------------------------------------------------------------------------------------------------
function point(x, y, z)
/*
Given a (x, y, z) surface point, returns the 3 x 1 vector form of the point.
*/
{
return [x, y, z]; // Return a 3 x 1 vector representing a traditional (x, y, z) surface point. This vector form eases matrix multiplication.
}
// -----------------------------------------------------------------------------------------------------
function Surface()
/*
A surface is a list of (x, y, z) points, in 3 x 1 vector format. This is a constructor function.
*/
{
this.points = [];
// An array of surface points in vector format. That is, each element of this array is a 3 x 1 array, as in [ [x1, y1, z1], [x2, y2, z2], [x3, y3, z3], ... ]
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.equation = function(x, y)
/*
Given the point (x, y), returns the associated z-coordinate based on the provided surface equation, of the form z = f(x, y).
*/
{
var d = Math.sqrt(x*x + y*y); // The distance d of the xy-point from the z-axis.
return 4*(Math.sin(d) / d); // Return the z-coordinate for the point (x, y, z).
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.generate = function()
/*
Creates a list of (x, y, z) points (in 3 x 1 vector format) representing the surface.
*/
{
var i = 0;
for (var x = constants.xMin; x <= constants.xMax; x += constants.xDelta)
{
for (var y = constants.yMin; y <= constants.yMax; y += constants.yDelta)
{
this.points[i] = point(x, y, this.equation(x, y)); // Store a surface point (in vector format) into the list of surface points.
++i;
}
}
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.color = function()
/*
The color of a surface point is a function of its z-coordinate height.
*/
{
var z; // The z-coordinate for a given surface point (x, y, z).
this.zMin = this.zMax = this.points[0][Z]; // A starting value. Note that zMin and zMax are custom properties that could possibly be useful if this code is extended later.
for (var i = 0; i < this.points.length; i++)
{
z = this.points[i][Z];
if (z < this.zMin) { this.zMin = z; }
if (z > this.zMax) { this.zMax = z; }
}
var zDelta = Math.abs(this.zMax - this.zMin) / constants.colorMap.length;
for (var i = 0; i < this.points.length; i++)
{
this.points[i].color = constants.colorMap[ Math.floor( (this.points[i][Z]-this.zMin)/zDelta ) ];
}
/* Note that the prior FOR loop is functionally equivalent to the follow (much less elegant) loop:
for (var i = 0; i < this.points.length; i++)
{
if (this.points[i][Z] <= this.zMin + zDelta) {this.points[i].color = "#060";}
else if (this.points[i][Z] <= this.zMin + 2*zDelta) {this.points[i].color = "#090";}
else if (this.points[i][Z] <= this.zMin + 3*zDelta) {this.points[i].color = "#0C0";}
else if (this.points[i][Z] <= this.zMin + 4*zDelta) {this.points[i].color = "#0F0";}
else if (this.points[i][Z] <= this.zMin + 5*zDelta) {this.points[i].color = "#9F0";}
else if (this.points[i][Z] <= this.zMin + 6*zDelta) {this.points[i].color = "#9C0";}
else if (this.points[i][Z] <= this.zMin + 7*zDelta) {this.points[i].color = "#990";}
else if (this.points[i][Z] <= this.zMin + 8*zDelta) {this.points[i].color = "#960";}
else if (this.points[i][Z] <= this.zMin + 9*zDelta) {this.points[i].color = "#930";}
else if (this.points[i][Z] <= this.zMin + 10*zDelta) {this.points[i].color = "#900";}
else {this.points[i].color = "#C00";}
}
*/
}
// -----------------------------------------------------------------------------------------------------
function update(){
document.querySelector("#xa").innerHTML = xangle;
document.querySelector("#ya").innerHTML = yangle;
document.querySelector("#za").innerHTML = zangle;
}
function appendCanvasElement()
/*
Creates and then appends the "myCanvas" canvas element to the DOM.
*/
{
var canvasElement = document.createElement('canvas');
canvasElement.width = constants.canvasWidth;
canvasElement.height = constants.canvasHeight;
canvasElement.id = "myCanvas";
canvasElement.getContext('2d').translate(constants.canvasWidth/2, constants.canvasHeight/2); // Translate the surface's origin to the center of the canvas.
document.body.appendChild(canvasElement); // Make the canvas element a child of the body element.
}
//------------------------------------------------------------------------------------------------------
Surface.prototype.sortByZIndex = function(A, B)
{
return A[Z] - B[Z]; // Determines if point A is behind, in front of, or at the same level as point B (with respect to the z-axis).
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.draw = function()
{
var myCanvas = document.getElementById("myCanvas"); // Required for Firefox.
var ctx = myCanvas.getContext("2d");
var res;
var xm;
// this.points = surface.points.sort(surface.sortByZIndex); // Sort the set of points based on relative z-axis position. If the points are visibly small, you can sort of get away with removing this step.
for (var i = 0; i < this.points.length; i++)
{
ctx.fillStyle = this.points[i].color;
ctx.fillRect(this.points[i][X] * constants.surfaceScale, this.points[i][Y] * constants.surfaceScale, constants.pointWidth, constants.pointWidth);
}
var c=document.getElementById("myCanvas");
var ctx=c.getContext("2d");
ctx.font="12px Arial";
ctx.fillStyle = "#000000";
ctx.fillText("X",this.points[p1][X] * constants.surfaceScale, this.points[p1][Y] * constants.surfaceScale);
var c=document.getElementById("myCanvas");
var ctx1=c.getContext("2d");
ctx1.font="12px Arial";
ctx1.fillText("Y",this.points[p2][X] * constants.surfaceScale, this.points[p2][Y] * constants.surfaceScale);
var c=document.getElementById("myCanvas");
var ctx1=c.getContext("2d");
ctx1.font="12px Arial";
ctx1.fillText("Z",this.points[p3][X] * constants.surfaceScale, this.points[p3][Y] * constants.surfaceScale);
var c=document.getElementById("myCanvas");
var ctx1=c.getContext("2d");
ctx1.font="12px Arial";
ctx1.fillText("-Y",this.points[p4][X] * constants.surfaceScale, this.points[p4][Y] * constants.surfaceScale);
var c=document.getElementById("myCanvas");
var ctx1=c.getContext("2d");
ctx1.font="12px Arial";
ctx1.fillText("-Z",this.points[p5][X] * constants.surfaceScale, this.points[p5][Y] * constants.surfaceScale);
var c=document.getElementById("myCanvas");
var ctx1=c.getContext("2d");
ctx1.font="12px Arial";
ctx1.fillText("-X",this.points[p6][X] * constants.surfaceScale, this.points[p6][Y] * constants.surfaceScale);
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.multi = function(R)
/*
Assumes that R is a 3 x 3 matrix and that this.points (i.e., P) is a 3 x n matrix. This method performs P = R * P.
*/
{
var Px = 0, Py = 0, Pz = 0; // Variables to hold temporary results.
var P = this.points; // P is a pointer to the set of surface points (i.e., the set of 3 x 1 vectors).
var sum; // The sum for each row/column matrix product.
for (var V = 0; V < P.length; V++) // For all 3 x 1 vectors in the point list.
{
Px = P[V][X], Py = P[V][Y], Pz = P[V][Z];
for (var Rrow = 0; Rrow < 3; Rrow++) // For each row in the R matrix.
{
sum = (R[Rrow][X] * Px) + (R[Rrow][Y] * Py) + (R[Rrow][Z] * Pz);
P[V][Rrow] = sum;
}
}
}
Surface.prototype.multipt = function(R)
/*
Assumes that R is a 3 x 3 matrix and that this.points (i.e., P) is a 3 x n matrix. This method performs P = R * P.
*/
{
var Px = 0, Py = 0, Pz = 0; // Variables to hold temporary results.
var P = this.points; // P is a pointer to the set of surface points (i.e., the set of 3 x 1 vectors).
var sum; // The sum for each row/column matrix product.
for (var V = P.length-1; V < P.length; V++) // For all 3 x 1 vectors in the point list.
{
Px = P[V][X], Py = P[V][Y], Pz = P[V][Z];
for (var Rrow = 0; Rrow < 3; Rrow++) // For each row in the R matrix.
{
sum = (R[Rrow][X] * Px) + (R[Rrow][Y] * Py) + (R[Rrow][Z] * Pz);
P[V][Rrow] = sum;
}
}
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.erase = function()
{
var myCanvas = document.getElementById("myCanvas"); // Required for Firefox.
var ctx = myCanvas.getContext("2d");
ctx.clearRect(-constants.canvasWidth/2, -constants.canvasHeight/2, myCanvas.width, myCanvas.height);
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.xRotate = function(sign)
/*
Assumes "sign" is either 1 or -1, which is used to rotate the surface "clockwise" or "counterclockwise".
*/
{
var Rx = [ [0, 0, 0],
[0, 0, 0],
[0, 0, 0] ]; // Create an initialized 3 x 3 rotation matrix.
Rx[0][0] = 1;
Rx[0][1] = 0; // Redundant but helps with clarity.
Rx[0][2] = 0;
Rx[1][0] = 0;
Rx[1][1] = Math.cos( sign*constants.dTheta );
Rx[1][2] = -Math.sin( sign*constants.dTheta );
Rx[2][0] = 0;
Rx[2][1] = Math.sin( sign*constants.dTheta );
Rx[2][2] = Math.cos( sign*constants.dTheta );
this.multi(Rx); // If P is the set of surface points, then this method performs the matrix multiplcation: Rx * P
this.erase(); // Note that one could use two canvases to speed things up, which also eliminates the need to erase.
this.draw();
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.yRotate = function(sign)
/*
Assumes "sign" is either 1 or -1, which is used to rotate the surface "clockwise" or "counterclockwise".
*/
{
var Ry = [ [0, 0, 0],
[0, 0, 0],
[0, 0, 0] ]; // Create an initialized 3 x 3 rotation matrix.
Ry[0][0] = Math.cos( sign*constants.dTheta );
Ry[0][1] = 0; // Redundant but helps with clarity.
Ry[0][2] = Math.sin( sign*constants.dTheta );
Ry[1][0] = 0;
Ry[1][1] = 1;
Ry[1][2] = 0;
Ry[2][0] = -Math.sin( sign*constants.dTheta );
Ry[2][1] = 0;
Ry[2][2] = Math.cos( sign*constants.dTheta );
this.multi(Ry); // If P is the set of surface points, then this method performs the matrix multiplcation: Rx * P
this.erase(); // Note that one could use two canvases to speed things up, which also eliminates the need to erase.
this.draw();
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.zRotate = function(sign)
/*
Assumes "sign" is either 1 or -1, which is used to rotate the surface "clockwise" or "counterclockwise".
*/
{
var Rz = [ [0, 0, 0],
[0, 0, 0],
[0, 0, 0] ]; // Create an initialized 3 x 3 rotation matrix.
Rz[0][0] = Math.cos( sign*constants.dTheta );
Rz[0][1] = -Math.sin( sign*constants.dTheta );
Rz[0][2] = 0; // Redundant but helps with clarity.
Rz[1][0] = Math.sin( sign*constants.dTheta );
Rz[1][1] = Math.cos( sign*constants.dTheta );
Rz[1][2] = 0;
Rz[2][0] = 0
Rz[2][1] = 0;
Rz[2][2] = 1;
this.multi(Rz); // If P is the set of surface points, then this method performs the matrix multiplcation: Rx * P
this.erase(); // Note that one could use two canvases to speed things up, which also eliminates the need to erase.
this.draw();
}
Surface.prototype.xRotatept = function()
{
var Rx = [ [0, 0, 0],
[0, 0, 0],
[0, 0, 0] ];
Rx[0][0] = 1;
Rx[0][1] = 0;
Rx[0][2] = 0;
Rx[1][0] = 0;
Rx[1][1] = Math.cos(xangle);
Rx[1][2] = -Math.sin(xangle);
Rx[2][0] = 0;
Rx[2][1] = Math.sin(xangle);
Rx[2][2] = Math.cos(xangle);
this.multipt(Rx);
this.erase();
this.draw();
}
Surface.prototype.yRotatept = function()
{
var Ry = [ [0, 0, 0],
[0, 0, 0],
[0, 0, 0] ];
Ry[0][0] = Math.cos(yangle);
Ry[0][1] = 0;
Ry[0][2] = Math.sin(yangle);
Ry[1][0] = 0;
Ry[1][1] = 1;
Ry[1][2] = 0;
Ry[2][0] = -Math.sin(yangle);
Ry[2][1] = 0;
Ry[2][2] = Math.cos(yangle);
this.multipt(Ry);
this.erase();
this.draw();
}
Surface.prototype.zRotatept = function()
{
var Rz = [ [0, 0, 0],
[0, 0, 0],
[0, 0, 0] ];
Rz[0][0] = Math.cos(zangle);
Rz[0][1] = -Math.sin(zangle);
Rz[0][2] = 0;
Rz[1][0] = Math.sin(zangle);
Rz[1][1] = Math.cos(zangle);
Rz[1][2] = 0;
Rz[2][0] = 0
Rz[2][1] = 0;
Rz[2][2] = 1;
this.multipt(Rz);
this.erase();
this.draw();
}
// -----------------------------------------------------------------------------------------------------
function processKeyDown(evt)
{
if (evt.ctrlKey)
{
switch (evt.keyCode)
{
case constants.upArrow:
// No operation other than preventing the default behavior of the arrow key.
evt.preventDefault(); // This prevents the default behavior of the arrow keys, which is to scroll the browser window when scroll bars are present. The user can still scroll the window with the mouse.
break;
case constants.downArrow:
// No operation other than preventing the default behavior of the arrow key.
evt.preventDefault();
break;
case constants.leftArrow:
// console.log("ctrl+leftArrow");
zangle=zangle-0.05;
update();
if(zangle<=-2*Math.PI)
{
zangle=0;
}
surface.zRotate(-1); // The sign determines if the surface rotates "clockwise" or "counterclockwise".
evt.preventDefault();
break;
case constants.rightArrow:
// console.log("ctrl+rightArrow");
zangle=zangle+0.05;
update();
if(zangle>=2*Math.PI)
{
zangle=0;
}
surface.zRotate(1);
evt.preventDefault();
break;
}
return; // When the control key is pressed, only the left and right arrows have meaning, no need to process any other key strokes (i.e., bail now).
}
// Assert: The control key is not pressed.
switch (evt.keyCode)
{
case constants.upArrow:
// console.log("upArrow");
xangle=xangle+0.05;
update();
if(xangle>=2*Math.PI)
{
xangle=0;
}
surface.xRotate(1);
evt.preventDefault();
break;
case constants.downArrow:
// console.log("downArrow");
xangle=xangle-0.05;
update();
if(xangle<=-2*Math.PI)
{
xangle=0;
}
surface.xRotate(-1);
evt.preventDefault();
break;
case constants.leftArrow:
// console.log("leftArrow");
yangle=yangle-0.05;
update();
if(yangle<=-2*Math.PI)
{
yangle=0;
}
surface.yRotate(-1);
evt.preventDefault();
break;
case constants.rightArrow:
// console.log("rightArrow");
yangle=yangle+0.05;
update();
if(yangle>=2*Math.PI)
{
yangle=0;
}
surface.yRotate(1);
evt.preventDefault();
break;
}
}
// -----------------------------------------------------------------------------------------------------
Surface.prototype.plot = function(x, y, z)
/*
add the point (x, y, z) (in 3 x 1 vector format) to the surface.
*/
{
this.points.push(point(x, y, z)); // Store a surface point
var x=0;
for (var x = constants.xMin; x <= constants.xMax; x += constants.xDelta)
{
this.points.push(point(x, 0, 0));
}
p6=1;
p1=this.points.length-1;
p4=this.points.length;
/*var y=-0.2
for (var x = constants.xMax+1; x <= constants.xMax+2; x += constants.xDelta)
{
this.points.push(point(x, y, 0));
y=y+0.002
}*/
/*for (var x = constants.xMax+1; x <= constants.xMax+2; x += constants.xDelta)
{
this.points.push(point(11, 0, 0))
}*/
for (var x = constants.xMin; x <= constants.xMax; x += constants.yDelta)
{
this.points.push(point(0, x, 0));
}
p2=this.points.length-1;
p5=this.points.length;
for (var x = constants.xMin; x <= constants.xMax; x += constants.yDelta)
{
this.points.push(point(0,0,x));
}
p3=this.points.length-1;
}
Surface.prototype.plot1 = function(x, y, z)
/*
add the point (x, y, z) (in 3 x 1 vector format) to the surface.
*/
{
this.points.push(point(x, y, z)); // Store a surface point
surface.xRotatept();
surface.yRotatept();
surface.zRotatept();
this.draw();
}
function onloadInit()
{
appendCanvasElement(); // Create and append the canvas element to the DOM.
surface.draw(); // Draw the surface on the canvas.
document.addEventListener('keydown', processKeyDown, false); // Used to detect if the control key has been pressed.
}
// -----------------------------------------------------------------------------------------------------
//surface.generate(); // Creates the set of points reprsenting the surface. Must be called before color().
surface.plot(0,0,0);
surface.color(); // Based on the min and max z-coordinate values, chooses colors for each point based on the point's z-ccordinate value (i.e., height).
window.addEventListener('load', onloadInit, false); // Perform processing that must occur after the page has fully loaded.
</script>
</head>
<body>
<table align="center">
<tr><td>
<h5 style="color:#606">Enter the value of (X,Y,Z)</h5>
<input type="text" value="5" class="num-input" width="50" size="2" id="x-input">
<input type="text" value="5" class="num-input" width="50" size="2" id="y-input">
<input type="text" value="2" class="num-input" width="50" size="2" id="z-input">
<input type="button" value="Plot Point" onClick="surface.plot1(document.getElementById('x-input').value,document.getElementById('y-input').value,document.getElementById('z-input').value); ">
</td></tr></table>
<table align="center"> <tr><td>
<span id="xa">0</span>deg<br>
<span id="ya">0</span>deg<br>
<span id="za">0</span>deg</td></tr></table>
</body>
</html>
