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Jun 8th, 2006, 1:22 AM
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#1 |
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King of Portal
Join Date: Sep 2005
Posts: 439
Rep Power: 4
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3D Engine in PHP
Well I originally started this project in Flash but it didn't work out for some reason there. I actually posted that problem here. After looking at the code for a while I realized that my math worked out and that something was wrong with the way Flash accesses arrays, at least in my humble opinion. Nevertheless, I succeeded in creating the 3d engine in PHP and it outputs itself as a still image of the view of a cube with white lines for visible edges and gray lines for non-visible ones. It turned out pretty nice I think. It uses pretty much every matrix operation you can think of and that's how it's structured. Test it out and tell me what you think. I still have to make modifications to it in order to be able to import some other formats for objects like in the VRML language, but for now enjoy the cube, change some of the numbers around and see the result.
<?php
// Creates a virtual cube composed of polygons
$cube = new VirtualObject();
// Viewable screen dimensions
$width = 640;
$height = 480;
// Sets up the camera's orientation and its focal distance
$x = sqrt(2) / 2;
$focal = 500;
$a = array(
array(-$x, 0.5, -0.5, 0),
array($x, 0.5, -0.5, 0),
array(0, -$x, -$x, 0),
array(0, 0, 0, 1)
);
// The vector normal to the viewing plane and parallel to the viewing direction
$n2[0][0] = $a[0][2];
$n2[1][0] = $a[1][2];
$n2[2][0] = $a[2][2];
$n2[3][0] = 0;
// Invert camera's plane to allow for change of basis
$a = inverse($a);
// Displace camera to its position in the world
$a[0][3] = 150;
$a[1][3] = 150;
$a[2][3] = 300 * $x;
// Create two images
$image1 = imagecreate($width, $height);
$image2 = imagecreate($width, $height);
// Set the line thickness of each image
imagesetthickness($image1, 1);
imagesetthickness($image2, 1);
// Set the background colors for each image
$blue1 = imagecolorallocate($image1, 0, 0, 127);
$blue2 = imagecolorallocate($image2, 0, 0, 127);
// Define some colors for each image
$white = imagecolorallocate($image1, 255, 255, 255);
$gray = imagecolorallocate($image2, 127, 127, 127);
// Draw each polygon
for($i = 0; $i < $cube->getPolyCount(); $i++){
// Retrieve the polygons from the cube object
$points = $cube->getPolygon($i);
// Modify each point of the polygon so that its now distanced to the camera's center point
for($j = 0; $j < 3; $j++){
$points[0][$j][0] -= $a[$j][3];
$points[1][$j][0] -= $a[$j][3];
$points[2][$j][0] -= $a[$j][3];
}
// Determine the normal vector for each polygon
$n1 = crossProduct(addition($points[0], scale(-1, $points[1])), addition($points[2], scale(-1, $points[1])));
// Write each vector in terms of the camera's orientation (change of basis)
$points[0] = multiply($a, $points[0]);
$points[1] = multiply($a, $points[1]);
$points[2] = multiply($a, $points[2]);
// Determine the distortion due to perspective
$focus[0] = $focal / magnitude($points[0]);
$focus[1] = $focal / magnitude($points[1]);
$focus[2] = $focal / magnitude($points[2]);
// Transform the 3d points into 2d coordinates for drawing
$x0 = $width / 2 + ($points[0][0][0] * $focus[0]);
$x1 = $width / 2 + ($points[1][0][0] * $focus[1]);
$x2 = $width / 2 + ($points[2][0][0] * $focus[2]);
$y0 = $height / 2 + ($points[0][1][0] * $focus[0]);
$y1 = $height / 2 + ($points[1][1][0] * $focus[1]);
$y2 = $height / 2 + ($points[2][1][0] * $focus[2]);
// Determine the cosine of the angle between the viewing plane and the polygonal plane
$cosTheta = dotProduct($n1, $n2) / (magnitude($n1) * magnitude($n2));
if($cosTheta <= 0){
// White lines because these are the planes at the front of the object
imageline($image1, $x0, $y0, $x1, $y1, $white);
imageline($image1, $x1, $y1, $x2, $y2, $white);
// imageline($image1, $x2, $y2, $x0, $y0, $white); // Draws the final polygon line
}else{
// Gray lines because these are the planes at the reare of the object
imageline($image2, $x0, $y0, $x1, $y1, $gray);
imageline($image2, $x1, $y1, $x2, $y2, $gray);
// imageline($image2, $x2, $y2, $x0, $y0, $gray); // Draws the final polygon line
}
}
// Make transparent the background of the viewable polygon drawing
imagecolortransparent($image1, $blue1);
// Layer it over the non-viewable polygon drawing
imagecopymerge($image2, $image1, 0, 0, 0, 0, 640, 480, 100);
// Output the finished image
imagepng($image2);
// Destroy the images
imagedestroy($image1);
imagedestroy($image2);
// Computes the cross product of two vectors
// $a: a row or column vector
// $b: a row or column vector
function crossProduct($a, $b){
if(sizeof($a) == 1){ // Cross product of row vectors
return array( // Return the cross product of row vectors as a row vector
array( $a[0][1] * $b[0][2] - $a[0][2] * $b[0][1],
-1 * ($a[0][0] * $b[0][2] - $a[0][2] * $b[0][0]),
$a[0][0] * $b[0][1] - $a[0][1] * $b[0][0],
0
)
);
}else{ // Cross product of column vectors
return array( // Return the cross product of column vectors as a column vector
array($a[1][0] * $b[2][0] - $a[2][0] * $b[1][0]),
array(-1 * ($a[0][0] * $b[2][0] - $a[2][0] * $b[0][0])),
array($a[0][0] * $b[1][0] - $a[1][0] * $b[0][0]),
array(0)
);
}
}
// Computes the addition of two matrices
// $A: an m x n matrix
// $B: an m x n matrix
function addition($A, $B){
$M; // The added matrix
// Add the two matrices together
for($i = 0; $i < sizeof($A); $i++){
for($j = 0; $j < sizeof($A[0]); $j++){
$M[$i][$j] = $A[$i][$j] + $B[$i][$j];
}
}
return $M; // Return the added matrix
}
// Computes a random matrix
// $m: the row dimension
// $n: the column dimension
// $lower: the lower bound of random numbers
// $upper: the upper bound of random numbers
function randMatrix($m, $n, $lower, $upper){
$M; // A random matrix
// Generate the random matrix
for($i = 0; $i < $m; $i++){
for($j = 0; $j < $n; $j++){
$M[$i][$j] = rand($lower, $upper);
}
}
return $M; // Return the random matrix
}
// Computes the magnitude of a vector
// $a: a row or column vector
function magnitude($a){
$result = 0; // The magnitude of the vector
// Use the Pythagorean theorem to determine the vector's magnitude
for($i = 0; $i < sizeof($a); $i++){
for($j = 0; $j < sizeof($a[0]); $j++){
$result += pow($a[$i][$j], 2);
}
}
return sqrt($result); // Return the magnitude of the vector
}
// Computes the adjoint of a matrix
// $A: a square matrix
function adjoint($A){
return scale(determinant($A), inverse($A)); // Returns the adjoint of a matrix
}
// Computes a scaled matrix
// $k: a scalar number
// $A: an m x n matrix
function scale($k, $A){
// Scale the matrix by multiplying each entry by k
for($i = 0; $i < sizeof($A); $i++){
for($j = 0; $j < sizeof($A[0]); $j++){
$A[$i][$j] *= $k;
}
}
return $A; // Returns the scaled matrix
}
// Computes the determinant of a matrix
// $A: a square matrix
function determinant($A){
$determinant = 1; // The determinant of the matrix
$n = sizeof($A); // Dimension of the square matrix
$E = identity($n); // An elementary matrix
// Find the determinant of a matrix by performing elementary matrix operations
// on an augmented matrix through the use of elementary matrices in order
// to convert the matrix into upper triangular form
// Multiply the diagonals of the upper triangular matrix to arrive at the
// determinant, only elementary operations I and III are allowed on the matrix.
// If operation I is performed at any time, multiply the determinant by a -1.
for($j = 0; $j < $n; $j++){
for($i = $j; $i < $n; $i++){
if($i == $j){
if($A[$i][$j] == 0){
for($k = $j + 1; $k < $n; $k++){
if($A[$k][$j] != 0){
$swap = $A[$i];
$A[$i] = $A[$k];
$A[$k] = $swap;
$determinant *= -1;
$k = $n;
}
}
}
$determinant *= $A[$i][$j];
}else{
$E[$i][$j] = -$A[$i][$j] / $A[$j][$j];
}
$A = multiply($E, $A);
$E = identity($n);
}
}
return $determinant; // Return the determinant of the matrix
}
// Computes the inverse of a matrix
// $A: a square matrix
function inverse($A){
$n = sizeof($A); // Dimension of the square matrix
$V = identity($n); // The inverse of the matrix
$E = identity($n); // An elementary matrix
// Find the inverse matrix by performing elementary matrix operations
// on an augmented matrix through the use of elementary matrices
for($j = 0; $j < $n; $j++){
for($i = $j; $i < $n; $i++){
if($i == $j){
if($A[$i][$j] == 0){
for($k = $j + 1; $k < $n; $k++){
if($A[$k][$j] != 0){
$swap = $A[$i];
$A[$i] = $A[$k];
$A[$k] = $swap;
$swap = $V[$i];
$V[$i] = $V[$k];
$V[$k] = $swap;
$k = $n;
}
}
}
$E[$i][$j] = 1 / $A[$i][$j];
}else{
$E[$i][$j] = -$A[$i][$j];
}
$A = multiply($E, $A);
$V = multiply($E, $V);
$E = identity($n);
}
}
for($j = $n - 1; $j > 0; $j--){
for($i = $j - 1; $i > -1; $i--){
$E[$i][$j] = -$A[$i][$j];
$A = multiply($E, $A);
$V = multiply($E, $V);
$E = identity($n);
}
}
return $V; // Return the inverse matrix
}
// Computes the product of a matrix multiplication
// $A: An m x n matrix
// $B: An n x o matrix
function multiply($A, $B){
$M; // The product of the multiplication
$B = transpose($B); // Transpose the second matrix
// Do the multiplication by making use of the dot product
for($i = 0; $i < sizeof($A); $i++){
for($j = 0; $j < sizeof($B); $j++){
$M[$i][$j] = dotProduct(array($A[$i]), array($B[$j]));
}
}
return $M; // Return the product
}
// Computes the dot product of two vectors
// $a: a row or column vector
// $b; a row or column vector
function dotProduct($a, $b){
$result = 0; // The result of the dot product
// The dot product
for($i = 0; $i < sizeof($a); $i++){
for($j = 0; $j < sizeof($a[0]); $j++){
$result += $a[$i][$j] * $b[$i][$j];
}
}
return $result; // Return the dot product
}
// Computes the transpose of a matrix
// $A: the matrix to be transposed
function transpose($A){
$T; // Transpose matrix
// Switch the i,jth entry to the j,ith entry
for($i = 0; $i < sizeof($A); $i++){
for($j = 0; $j < sizeof($A[0]); $j++){
$T[$j][$i] = $A[$i][$j];
}
}
return $T; // Return the transpose matrix
}
// Computes an identity matrix of size n x n
// $n: size of the matrix wanted
function identity($n){
$I; // Identity matrix
// Fill the matrices diagonal with 1's and everything else with 0's
for($i = 0; $i < $n; $i++){
for($j = 0; $j < $n; $j++){
if($i == $j){
$I[$i][$j] = 1;
}else{
$I[$i][$j] = 0;
}
}
}
return $I; // Return the identity matrix
}
class VirtualObject{
// Member declarations
private $polyObject;
// Constructor
function __construct(){
$this->polyObject =
array( // object
array( // polygon
array( // vector
array(50),
array(-50),
array(50),
array(0)
),
array( // vector
array(-50),
array(-50),
array(50),
array(0)
),
array( // vector
array(-50),
array(50),
array(50),
array(0)
)
),
array( // polygon
array( // vector
array(-50),
array(50),
array(50),
array(0)
),
array( // vector
array(50),
array(50),
array(50),
array(0)
),
array( // vector
array(50),
array(-50),
array(50),
array(0)
)
),
array( // polygon
array( // vector
array(50),
array(-50),
array(-50),
array(0)
),
array( // vector
array(50),
array(-50),
array(50),
array(0)
),
array( // vector
array(50),
array(50),
array(50),
array(0)
)
),
array( // polygon
array( // vector
array(50),
array(50),
array(50),
array(0)
),
array( // vector
array(50),
array(50),
array(-50),
array(0)
),
array( // vector
array(50),
array(-50),
array(-50),
array(0)
)
),
array( // polygon
array( // vector
array(50),
array(50),
array(-50),
array(0)
),
array( // vector
array(50),
array(50),
array(50),
array(0)
),
array( // vector
array(-50),
array(50),
array(50),
array(0)
)
),
array( // polygon
array( // vector
array(-50),
array(50),
array(50),
array(0)
),
array( // vector
array(-50),
array(50),
array(-50),
array(0)
),
array( // vector
array(50),
array(50),
array(-50),
array(0)
)
),
array( // polygon
array( // vector
array(-50),
array(-50),
array(-50),
array(0)
),
array( // vector
array(50),
array(-50),
array(-50),
array(0)
),
array( // vector
array(50),
array(50),
array(-50),
array(0)
)
),
array( // polygon
array( // vector
array(50),
array(50),
array(-50),
array(0)
),
array( // vector
array(-50),
array(50),
array(-50),
array(0)
),
array( // vector
array(-50),
array(-50),
array(-50),
array(0)
)
),
array( // polygon
array( // vector
array(-50),
array(50),
array(-50),
array(0)
),
array( // vector
array(-50),
array(50),
array(50),
array(0)
),
array( // vector
array(-50),
array(-50),
array(50),
array(0)
)
),
array( // polygon
array( // vector
array(-50),
array(-50),
array(50),
array(0)
),
array( // vector
array(-50),
array(-50),
array(-50),
array(0)
),
array( // vector
array(-50),
array(50),
array(-50),
array(0)
)
),
array( // polygon
array( // vector
array(-50),
array(-50),
array(-50),
array(0)
),
array( // vector
array(-50),
array(-50),
array(50),
array(0)
),
array( // vector
array(50),
array(-50),
array(50),
array(0)
)
),
array( // polygon
array( // vector
array(50),
array(-50),
array(50),
array(0)
),
array( // vector
array(50),
array(-50),
array(-50),
array(0)
),
array( // vector
array(-50),
array(-50),
array(-50),
array(0)
)
)
);
}
// Method declarations
// Returns the polygon count of the object
public function getPolyCount(){
return sizeof($this->polyObject);
}
// Returns a particular polygon of the object
public function getPolygon($n){
return $this->polyObject[$n];
}
}
?>
__________________
Lo, there do I see my father. 'Lo, there do I see My mother, and my sisters, and my brothers. 'Lo, there do I see The line of my people... Back to the beginning. 'Lo, they do call to me. They bid me take my place among them. In the halls of Valhalla... Where the brave... May live... ...forever.. GrimBB | Mimesis |
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Jun 8th, 2006, 3:10 AM
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#2 |
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Unverified User
Join Date: Aug 2005
Location: none
Posts: 146
Rep Power: 0
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Very exotic for PHP.
__________________
Warning: My posts may change (dramatically) within the first 15 minutes they're posted. Got 'Nux?—GNU/Linux and other free software support. It's GNU/Linux, not just Linux. |
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Jun 8th, 2006, 4:12 AM
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#3 | |
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Hobbyist Programmer
Join Date: Mar 2006
Location: WA, USA
Posts: 343
Rep Power: 3
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i get this error when i try to run it on my php 5 server.
Quote:
28 // Create two images 29 $image1 = imagecreate($width, $height); 30 $image2 = imagecreate($width, $height);
__________________
i dont know much about programming but i try to help |
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Jun 8th, 2006, 6:27 PM
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#4 | |
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Hobbyist Programmer
Join Date: Feb 2006
Posts: 214
Rep Power: 0
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I got an error too.
Quote:
__________________
Death smiles at us all. All a man can do is smile back. |
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Jun 8th, 2006, 9:19 PM
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#5 |
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King of Portal
Join Date: Sep 2005
Posts: 439
Rep Power: 4
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Mrynit I think your error may be that the graphical functions for PHP aren't installed on your system. Check the PHP manual and look at the Image Functions section. So you need to find out how to install them, since it says they're undefined. That's just a theory though I'm not entirely sure.
Eric The Red, I have NO idea what your error is so I can't offer you a fix. I can however show you what the output of the program is.
__________________
Lo, there do I see my father. 'Lo, there do I see My mother, and my sisters, and my brothers. 'Lo, there do I see The line of my people... Back to the beginning. 'Lo, they do call to me. They bid me take my place among them. In the halls of Valhalla... Where the brave... May live... ...forever.. GrimBB | Mimesis |
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Jun 9th, 2006, 11:33 AM
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#6 |
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PFO Founder
  
Join Date: Mar 2004
Location: Fargo, ND
Posts: 1,667
Rep Power: 10
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Well I must be missing something on my server because this is what I get
http://www.kylekonline.com/test/newtest.php
__________________
BIG K aka Kyle Programming Forums Kyle K Online Please do not PM or email me programming questions. Post them in the forums instead. |
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Jun 9th, 2006, 11:40 AM
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#7 | |
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Programming Guru
Join Date: May 2004
Location: Brandon, Manitoba, Canada
Posts: 2,023
Rep Power: 7
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Quote:
you need to have GD enabled. looks pretty cool though, what are you planning on coding with it (if anything at all)?
__________________
Profanity is the one language that all programmers understand. Check out my Blog <---updated Nov 30 2007! |
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Jun 9th, 2006, 2:41 PM
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#8 |
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King of Portal
Join Date: Sep 2005
Posts: 439
Rep Power: 4
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I'm confused, when I looked at your page big k everything looked in order.
 I'm not really planning on doing anything much with it Pizentios, I was just curious to undertake the mathematics behind such a thing since I'd never quite understood how people achieved the effect. There's also some stuff in there which isn't quite right, like if it so happens that a point is located at the camera's center point the program will crash because of a division by 0 which I have to fix with a try catch routine or something. The matrix subroutines should also catch some errors, like if dimensions don't match for certain cases, and for instance if a matrix is singular (that it has no inverse), in which case changing the basis would be impossible. I'm not quite sure how that would work. I know some people place their camera at the world origin and then translate everything accordingly, but that didn't seem very realistic, since every object in the world should move independently, but that's just my own opinion. And I'm not too sure how to achieve the planar projections without performing a change of basis. Perhaps some sort of vector subtraction or addition I don't know, also programming object interactions and rotations as well as translations on the fly I'm still not so sure how to achieve. But if I do I'll post it up here rest assured.
__________________
Lo, there do I see my father. 'Lo, there do I see My mother, and my sisters, and my brothers. 'Lo, there do I see The line of my people... Back to the beginning. 'Lo, they do call to me. They bid me take my place among them. In the halls of Valhalla... Where the brave... May live... ...forever.. GrimBB | Mimesis |
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Jun 9th, 2006, 5:48 PM
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#9 | |
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Unverified User
Join Date: Aug 2005
Location: none
Posts: 146
Rep Power: 0
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Quote:
__________________
Warning: My posts may change (dramatically) within the first 15 minutes they're posted. Got 'Nux?—GNU/Linux and other free software support. It's GNU/Linux, not just Linux. |
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Jun 11th, 2006, 3:51 AM
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#10 |
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Hobbyist Programmer
Join Date: Oct 2005
Location: Indiana
Posts: 224
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Nifty program. I'd suggest this be moved to the Finished Projects section . I might play with your code if you don't mind. It would be neat for it to take a text file as input and then render the object
__________________
#programmingforums relay - http://thegupstudio.com/cgi-bin/pforelay.cgi freelance scripts - http://ryanguthrie.com/index.html |
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