<meta charset="utf-8">

<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">

<title>WebGL2 - 2D Geometry Matrix Transform with Projection</title>

<link type="text/css" href="resources/webgl-tutorials.css" rel="stylesheet" />

<div class="description">

Drag sliders to translate, rotate, and scale.

</div>

<canvas id="canvas"></canvas>

<div id="uiContainer">

<div id="ui">

<div id="cameraAngle"></div>

</div>

</div>

<script src="resources/webgl-utils.js"></script>

<script src="resources/webgl-lessons-ui.js"></script>

"use strict";

var vertexShaderSource = `#version 300 es

var fragmentShaderSource = `#version 300 es

function main() {

// Get A WebGL context

/** @type {HTMLCanvasElement} */

var canvas = document.querySelector("#canvas");

var gl = canvas.getContext("webgl2");

if (!gl) {

return;

}

// Use our boilerplate utils to compile the shaders and link into a program

var program = webglUtils.createProgramFromSources(gl,

[vertexShaderSource, fragmentShaderSource]);

// look up where the vertex data needs to go.

var positionAttributeLocation = gl.getAttribLocation(program, "a_position");

// look up uniform locations

var matrixLocation = gl.getUniformLocation(program, "u_matrix");

var colorAttributeLocation = gl.getAttribLocation(program, "a_color");

// Create a buffer

var positionBuffer = gl.createBuffer();

// Create a vertex array object (attribute state)

var vao = gl.createVertexArray();

// and make it the one we're currently working with

gl.bindVertexArray(vao);

// Turn on the attribute

gl.enableVertexAttribArray(positionAttributeLocation);

// Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = positionBuffer)

gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);

// Set Geometry.

setGeometry(gl);

// Tell the attribute how to get data out of positionBuffer (ARRAY_BUFFER)

var size = 3; // 3 components per iteration

var type = gl.FLOAT; // the data is 32bit floats

var normalize = false; // don't normalize the data

var stride = 0; // 0 = move forward size * sizeof(type) each iteration to get the next position

var offset = 0; // start at the beginning of the buffer

gl.vertexAttribPointer(

positionAttributeLocation, size, type, normalize, stride, offset);

// create the color buffer, make it the current ARRAY_BUFFER

// and copy in the color values

var colorBuffer = gl.createBuffer();

gl.bindBuffer(gl.ARRAY_BUFFER, colorBuffer);

setColors(gl);

// Turn on the attribute

gl.enableVertexAttribArray(colorAttributeLocation);

// Tell the attribute how to get data out of colorBuffer (ARRAY_BUFFER)

var size = 3; // 3 components per iteration

var type = gl.UNSIGNED_BYTE; // the data is 8bit unsigned bytes

var normalize = true; // convert from 0-255 to 0.0-1.0

var stride = 0; // 0 = move forward size * sizeof(type) each

// iteration to get the next color

var offset = 0; // start at the beginning of the buffer

gl.vertexAttribPointer(

colorAttributeLocation, size, type, normalize, stride, offset);

function radToDeg(r) {

return r * 180 / Math.PI;

}

function degToRad(d) {

return d * Math.PI / 180;

}

// Variable to setup the projectionViewMatrix and interaction

var fieldOfViewRadians = degToRad(60);

var cameraAngleRadians = degToRad(0);

drawScene();

// Setup a ui.

webglLessonsUI.setupSlider("#cameraAngle", { value: radToDeg(cameraAngleRadians), slide: updateCameraAngle, min: -360, max: 360 });

function updateCameraAngle(event, ui) {

cameraAngleRadians = degToRad(ui.value);

drawScene();

}

// Draw the scene.

function drawScene() {

webglUtils.resizeCanvasToDisplaySize(gl.canvas);

// Tell WebGL how to convert from clip space to pixels

gl.viewport(0, 0, gl.canvas.width, gl.canvas.height);

// Clear the canvas

gl.clearColor(0, 0, 0, 0);

gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);

// tell webgl to cull faces

gl.enable(gl.CULL_FACE);

gl.enable(gl.DEPTH_TEST);

// Tell it to use our program (pair of shaders)

gl.useProgram(program);

// Bind the attribute/buffer set we want.

gl.bindVertexArray(vao);

// Compute the matrix. This part mimic the implementation of the OpenGL pipeline.

// Documentation:

// http://www.songho.ca/opengl/gl_transform.html

// https://learnopengl.com/Getting-started/Coordinate-Systems

var aspect = gl.canvas.clientWidth / gl.canvas.clientHeight;

var zNear = 1;

var zFar = 2000;

var projectionMatrix = m4.perspective(fieldOfViewRadians, aspect, zNear, zFar);

var radius = 200;

// Compute the position of the first F

var fPosition = [radius, 0, 0];

// Setup the cameraMatrix which is the inverse of the viewMatrix

var cameraMatrix = m4.yRotation(cameraAngleRadians);

cameraMatrix = m4.translate(cameraMatrix, 0, 50, radius * 1.5);

// Get the camera's position from the matrix we computed

var cameraPosition = [

cameraMatrix[3],

cameraMatrix[7],

cameraMatrix[11],

];

var up = [0, 1, 0];

// Compute the camera's matrix using look at.

var cameraMatrix = m4.lookAt(cameraPosition, fPosition, up);

// Make a viewMatrix from the camera matrix.

var viewMatrix = m4.inverse(cameraMatrix);

var viewProjectionMatrix = m4.multiply(projectionMatrix, viewMatrix);

var numFs = 5;

// Draw 'F's in a circle

for (var ii = 0; ii < numFs; ++ii) {

var angle = ii * Math.PI * 2 / numFs;

var x = Math.cos(angle) * radius;

var z = Math.sin(angle) * radius;

// add in the translation for this F

// http://www.songho.ca/opengl/gl_transform.html

var translationMatrix = m4.translation(x, 0, z);

// As the origin geometry has been setup in a 2D mode (Y+ toward the bottom)

// some operation are made to position the model correctly in 3D space

var modelMatrix = m4.identity;

modelMatrix = m4.xRotate(modelMatrix, Math.PI);

modelMatrix = m4.translate(modelMatrix, -50, -75, -15);

var matrix = m4.multiply(viewProjectionMatrix,

translationMatrix, modelMatrix);

// Set the matrix.

gl.uniformMatrix4fv(matrixLocation, true, matrix);

// Draw the geometry.

var primitiveType = gl.TRIANGLES;

var offset = 0;

var count = 16 * 6;

gl.drawArrays(primitiveType, offset, count);

}

}

}

function print(a) {

console.log("" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3]);

console.log("" + a[4] + ", " + a[5] + ", " + a[6] + ", " + a[7]);

console.log("" + a[8] + ", " + a[9] + ", " + a[10] + ", " + a[11]);

console.log("" + a[12] + ", " + a[13] + ", " + a[14] + ", " + a[15]);

}

// Fill the current ARRAY_BUFFER buffer

// with the values that define a letter 'F'.

function setGeometry(gl) {

gl.bufferData(

gl.ARRAY_BUFFER,

new Float32Array([

// left column front

0, 0, 0,

0, 150, 0,

30, 0, 0,

0, 150, 0,

30, 150, 0,

30, 0, 0,

// top rung front

30, 0, 0,

30, 30, 0,

100, 0, 0,

30, 30, 0,

100, 30, 0,

100, 0, 0,

// middle rung front

30, 60, 0,

30, 90, 0,

67, 60, 0,

30, 90, 0,

67, 90, 0,

67, 60, 0,

// left column back

0, 0, 30,

30, 0, 30,

0, 150, 30,

0, 150, 30,

30, 0, 30,

30, 150, 30,

// top rung back

30, 0, 30,

100, 0, 30,

30, 30, 30,

30, 30, 30,

100, 0, 30,

100, 30, 30,

// middle rung back

30, 60, 30,

67, 60, 30,

30, 90, 30,

30, 90, 30,

67, 60, 30,

67, 90, 30,

// top

0, 0, 0,

100, 0, 0,

100, 0, 30,

0, 0, 0,

100, 0, 30,

0, 0, 30,

// top rung right

100, 0, 0,

100, 30, 0,

100, 30, 30,

100, 0, 0,

100, 30, 30,

100, 0, 30,

// under top rung

30, 30, 0,

30, 30, 30,

100, 30, 30,

30, 30, 0,

100, 30, 30,

100, 30, 0,

// between top rung and middle

30, 30, 0,

30, 60, 30,

30, 30, 30,

30, 30, 0,

30, 60, 0,

30, 60, 30,

// top of middle rung

30, 60, 0,

67, 60, 30,

30, 60, 30,

30, 60, 0,

67, 60, 0,

67, 60, 30,

// right of middle rung

67, 60, 0,

67, 90, 30,

67, 60, 30,

67, 60, 0,

67, 90, 0,

67, 90, 30,

// bottom of middle rung.

30, 90, 0,

30, 90, 30,

67, 90, 30,

30, 90, 0,

67, 90, 30,

67, 90, 0,

// right of bottom

30, 90, 0,

30, 150, 30,

30, 90, 30,

30, 90, 0,

30, 150, 0,

30, 150, 30,

// bottom

0, 150, 0,

0, 150, 30,

30, 150, 30,

0, 150, 0,

30, 150, 30,

30, 150, 0,

// left side

0, 0, 0,

0, 0, 30,

0, 150, 30,

0, 0, 0,

0, 150, 30,

0, 150, 0,

]),

gl.STATIC_DRAW);

}

// Fill the current ARRAY_BUFFER buffer with colors for the 'F'.

function setColors(gl) {

gl.bufferData(

gl.ARRAY_BUFFER,

new Uint8Array([

// left column front

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

// top rung front

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

// middle rung front

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

200, 70, 120,

// left column back

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

// top rung back

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

// middle rung back

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

80, 70, 200,

// top

70, 200, 210,

70, 200, 210,

70, 200, 210,

70, 200, 210,

70, 200, 210,

70, 200, 210,

// top rung right

200, 200, 70,

200, 200, 70,

200, 200, 70,

200, 200, 70,

200, 200, 70,

200, 200, 70,

// under top rung

210, 100, 70,

210, 100, 70,

210, 100, 70,

210, 100, 70,

210, 100, 70,

210, 100, 70,

// between top rung and middle

210, 160, 70,

210, 160, 70,

210, 160, 70,

210, 160, 70,

210, 160, 70,

210, 160, 70,

// top of middle rung

70, 180, 210,

70, 180, 210,

70, 180, 210,

70, 180, 210,

70, 180, 210,

70, 180, 210,

// right of middle rung

100, 70, 210,

100, 70, 210,

100, 70, 210,

100, 70, 210,

100, 70, 210,

100, 70, 210,

// bottom of middle rung.

76, 210, 100,

76, 210, 100,

76, 210, 100,

76, 210, 100,

76, 210, 100,

76, 210, 100,

// right of bottom

140, 210, 80,

140, 210, 80,

140, 210, 80,

140, 210, 80,

140, 210, 80,

140, 210, 80,

// bottom

90, 130, 110,

90, 130, 110,

90, 130, 110,

90, 130, 110,

90, 130, 110,

90, 130, 110,

// left side

160, 160, 220,

160, 160, 220,

160, 160, 220,

160, 160, 220,

160, 160, 220,

160, 160, 220,

]),

gl.STATIC_DRAW);

}

var m4 = {

identity:

[

1, 0, 0, 0,

0, 1, 0, 0,

0, 0, 1, 0,

0, 0, 0, 1,

],

translation: function (tx, ty, tz) {

return [

1, 0, 0, tx,

0, 1, 0, ty,

0, 0, 1, tz,

0, 0, 0, 1,

];

},

xRotation: function (angleInRadians) {

var c = Math.cos(angleInRadians);

var s = Math.sin(angleInRadians);

return [

1, 0, 0, 0,

0, c, -s, 0,

0, s, c, 0,

0, 0, 0, 1,

];

},

yRotation: function (angleInRadians) {

var c = Math.cos(angleInRadians);

var s = Math.sin(angleInRadians);

return [

c, 0, -s, 0,

0, 1, 0, 0,

s, 0, c, 0,

0, 0, 0, 1,

];

},

zRotation: function (angleInRadians) {

var c = Math.cos(angleInRadians);

var s = Math.sin(angleInRadians);

return [

c, -s, 0, 0,

s, c, 0, 0,

0, 0, 1, 0,

0, 0, 0, 1,

];

},

scaling: function (sx, sy, sz) {

return [

sx, 0, 0, 0,

0, sy, 0, 0,

0, 0, sz, 0,

0, 0, 0, 1,

];

},

translate: function (m, tx, ty, tz) {

return m4.multiply(m, m4.translation(tx, ty, tz));

},

xRotate: function (m, angleInRadians) {

return m4.multiply(m, m4.xRotation(angleInRadians));

},

yRotate: function (m, angleInRadians) {

return m4.multiply(m, m4.yRotation(angleInRadians));

},

zRotate: function (m, angleInRadians) {

return m4.multiply(m, m4.zRotation(angleInRadians));

},

scale: function (m, sx, sy, sz) {

return m4.multiply(m, m4.scaling(sx, sy, sz));

},

// Give it an ugly name to avoid to use it outside

multiply2Matrices: function (a, b) {

let res = Array(4 * 4).fill(0);

for (let i = 0; i < 4; ++i) {

for (let j = 0; j < 4; ++j) {

let acc = 0;

for (let k = 0; k < 4; ++k) {

acc += a[i * 4 + k] * b[k * 4 + j];

}

res[i * 4 + j] = acc;

}

}

return res;

},

multiply: function () {

// Transform arguments to an array to be able to call reduce

let arrayArgs = Array.prototype.slice.call(arguments);

return arrayArgs.reduce(

(resMat, currentMat) => m4.multiply2Matrices(resMat, currentMat),

m4.identity);

},

projection: function (width, height, depth) {

// Note: This matrix flips the Y axis so 0 is at the top.

return [

2 / width, 0, 0, -1,

0, -2 / height, 0, 1,

0, 0, 2 / depth, 0,

0, 0, 0, 1,

];

},

orthographic: function (left, right, bottom, top, near, far) {

return [

2 / (right - left), 0, 0, (left + right) / (left - right),

0, 2 / (top - bottom), 0, (bottom + top) / (bottom - top),

// 0, 0, 2 / (near - far), (near + far) / (near - far),

0, 0, 2 / (far - near), (far + near) / (far - near),

0, 0, 0, 1,

];

},

// Documentation links:

// http://www.songho.ca/opengl/gl_projectionmatrix.html

// https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/opengl-perspective-projection-matrix

// https://stackoverflow.com/questions/28286057/trying-to-understand-the-math-behind-the-perspective-matrix-in-webgl/28301213#28301213

perspective: function (fieldOfViewInRadians, aspect, near, far) {

var f = Math.tan(0.5 * (Math.PI - fieldOfViewInRadians));

var rangeInv = 1.0 / (far - near);

return [

f / aspect, 0, 0, 0,

0, f, 0, 0,

0, 0, -(far + near) * rangeInv, -2 * near * far * rangeInv,

0, 0, -1, 0

];

},

inverse: function (m) {

var m00 = m[0 * 4 + 0];

var m01 = m[0 * 4 + 1];

var m02 = m[0 * 4 + 2];

var m03 = m[0 * 4 + 3];

var m10 = m[1 * 4 + 0];

var m11 = m[1 * 4 + 1];

var m12 = m[1 * 4 + 2];

var m13 = m[1 * 4 + 3];

var m20 = m[2 * 4 + 0];

var m21 = m[2 * 4 + 1];

var m22 = m[2 * 4 + 2];

var m23 = m[2 * 4 + 3];

var m30 = m[3 * 4 + 0];

var m31 = m[3 * 4 + 1];

var m32 = m[3 * 4 + 2];

var m33 = m[3 * 4 + 3];

var tmp_0 = m22 * m33;

var tmp_1 = m32 * m23;

var tmp_2 = m12 * m33;

var tmp_3 = m32 * m13;

var tmp_4 = m12 * m23;

var tmp_5 = m22 * m13;

var tmp_6 = m02 * m33;

var tmp_7 = m32 * m03;

var tmp_8 = m02 * m23;

var tmp_9 = m22 * m03;

var tmp_10 = m02 * m13;

var tmp_11 = m12 * m03;

var tmp_12 = m20 * m31;

var tmp_13 = m30 * m21;

var tmp_14 = m10 * m31;

var tmp_15 = m30 * m11;

var tmp_16 = m10 * m21;

var tmp_17 = m20 * m11;

var tmp_18 = m00 * m31;

var tmp_19 = m30 * m01;

var tmp_20 = m00 * m21;

var tmp_21 = m20 * m01;

var tmp_22 = m00 * m11;

var tmp_23 = m10 * m01;

var t0 = (tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31) -

(tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);

var t1 = (tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31) -

(tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);

var t2 = (tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31) -

(tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);

var t3 = (tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21) -

(tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);

var d = 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);

return [

d * t0,

d * t1,

d * t2,

d * t3,

d * ((tmp_1 * m10 + tmp_2 * m20 + tmp_5 * m30) -

(tmp_0 * m10 + tmp_3 * m20 + tmp_4 * m30)),

d * ((tmp_0 * m00 + tmp_7 * m20 + tmp_8 * m30) -

(tmp_1 * m00 + tmp_6 * m20 + tmp_9 * m30)),

d * ((tmp_3 * m00 + tmp_6 * m10 + tmp_11 * m30) -

(tmp_2 * m00 + tmp_7 * m10 + tmp_10 * m30)),

d * ((tmp_4 * m00 + tmp_9 * m10 + tmp_10 * m20) -

(tmp_5 * m00 + tmp_8 * m10 + tmp_11 * m20)),

d * ((tmp_12 * m13 + tmp_15 * m23 + tmp_16 * m33) -

(tmp_13 * m13 + tmp_14 * m23 + tmp_17 * m33)),

d * ((tmp_13 * m03 + tmp_18 * m23 + tmp_21 * m33) -

(tmp_12 * m03 + tmp_19 * m23 + tmp_20 * m33)),

d * ((tmp_14 * m03 + tmp_19 * m13 + tmp_22 * m33) -

(tmp_15 * m03 + tmp_18 * m13 + tmp_23 * m33)),

d * ((tmp_17 * m03 + tmp_20 * m13 + tmp_23 * m23) -

(tmp_16 * m03 + tmp_21 * m13 + tmp_22 * m23)),

d * ((tmp_14 * m22 + tmp_17 * m32 + tmp_13 * m12) -

(tmp_16 * m32 + tmp_12 * m12 + tmp_15 * m22)),

d * ((tmp_20 * m32 + tmp_12 * m02 + tmp_19 * m22) -

(tmp_18 * m22 + tmp_21 * m32 + tmp_13 * m02)),

d * ((tmp_18 * m12 + tmp_23 * m32 + tmp_15 * m02) -

(tmp_22 * m32 + tmp_14 * m02 + tmp_19 * m12)),

d * ((tmp_22 * m22 + tmp_16 * m02 + tmp_21 * m12) -

(tmp_20 * m12 + tmp_23 * m22 + tmp_17 * m02)),

];

},

lookAt: function (cameraPosition, target, up) {

var zAxis = normalize(

subtractVectors(cameraPosition, target));

var xAxis = normalize(cross(up, zAxis));

var yAxis = normalize(cross(zAxis, xAxis));

return [

xAxis[0], yAxis[0], zAxis[0], cameraPosition[0],

xAxis[1], yAxis[1], zAxis[1], cameraPosition[1],

xAxis[2], yAxis[2], zAxis[2], cameraPosition[2],

0, 0, 0, 1,

];

},

};

function cross(a, b) {

return [a[1] * b[2] - a[2] * b[1],

a[2] * b[0] - a[0] * b[2],

a[0] * b[1] - a[1] * b[0]];

}

function subtractVectors(a, b) {

return [a[0] - b[0], a[1] - b[1], a[2] - b[2]];

}

function normalize(v) {

var length = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);

// make sure we don't divide by 0.

if (length > 0.00001) {

return [v[0] / length, v[1] / length, v[2] / length];

} else {

return [0, 0, 0];

}

}

main();