Obracanie płótna o problemy z osią
Używam kanwy 3d do narysowania wykresu 3d, w którym mogę wykreślić punkty, takie jak (1,5,4), (-8,6, -2) itd. Tak więc jestem w stanie narysować wszystkie dodatnie i ujemne x, Oś y i z. Mam również efekt obrotu za pomocą klawiszy strzałek. Instrukcje dotyczące obracania: oś z rozciąga się od środka ekranu.
Aby obrócić wokół osi X, naciśnij klawisze strzałek w górę / w dół. Aby obrócić wokół osi Y, naciśnij klawisze strzałek w lewo / w prawo. Aby obrócić wokół osi Z, naciśnij klawisze Ctrl + Lewo / Ctrl + Strzałka w dół.
Mogę narysować punkt, określając punkty w podanym polu tekstowym. Teraz problem polega na tym, że na przykład, jeśli wykreślę (5,5,2), będzie on działał poprawnie. Ale jeśli najpierw obrócę oś x, a potem oś y, to punkt zostanie prawidłowo wykreślony. Problem pojawia się, gdy najpierw obracam oś y, a potem oś x. Punkt zostanie nieprawidłowo wykreślony. Łatwa metoda znalezienia napotkanego problemu: można to łatwo sprawdzić, jeśli kontynuujesz drukowanie tego samego punktu wielokrotnie. Punkt powinien być wykreślony powyżej tego samego punktu, tak aby widoczny był tylko pojedynczy punkt. Ale w moim przypadku ten sam punkt ( dla ex (5,5,2) jest rysowany w innym miejscu na płótnie podczas obracania. Ten problem pojawia się tylko wtedy, gdy najpierw obracam oś y, a potem oś x, albo jeśli najpierw obracam oś z, a potem oś y. to błąd, który popełniłem w kodowaniu. Jestem nowy w tym płótnie 3d i skrypcie java. Więc proszę o pomoc.
<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>