OrthoGraphic
2D는 3x3 Metrices 사용, 3D는 4x4 Metrices 사용
<canvas id="canvas"></canvas>
<div id="uiContainer">
<div id="ui">
<div id="x"></div>
<div id="y"></div>
<div id="z"></div>
<div id="angleX"></div>
<div id="angleY"></div>
<div id="angleZ"></div>
<div id="scaleX"></div>
<div id="scaleY"></div>
<div id="scaleZ"></div>
</div>
</div>
<!-- vertex shader -->
<script id="vertex-shader-3d" type="x-shader/x-vertex">
attribute vec4 a_position;
attribute vec4 a_color;
uniform mat4 u_matrix;
varying vec4 v_color;
void main() {
// Multiply the position by the matrix.
gl_Position = u_matrix * a_position;
// Pass the color to the fragment shader.
v_color = a_color;
}
</script>
<!-- fragment shader -->
<script id="fragment-shader-3d" type="x-shader/x-fragment">
precision mediump float;
// Passed in from the vertex shader.
varying vec4 v_color;
void main() {
gl_FragColor = v_color;
}
</script><!--
for most samples webgl-utils only provides shader compiling/linking and
canvas resizing because why clutter the examples with code that's the same in every sample.
See https://webglfundamentals.org/webgl/lessons/webgl-boilerplate.html
and https://webglfundamentals.org/webgl/lessons/webgl-resizing-the-canvas.html
for webgl-utils, m3, m4, and webgl-lessons-ui.
-->
<script src="https://webglfundamentals.org/webgl/resources/webgl-utils.js"></script>
<script src="https://webglfundamentals.org/webgl/resources/webgl-lessons-ui.js"></script>
"use strict";
function main() {
// Get A WebGL context
/** @type {HTMLCanvasElement} */
var canvas = document.querySelector("#canvas");
var gl = canvas.getContext("webgl");
if (!gl) {
return;
}
// setup GLSL program
var program = webglUtils.createProgramFromScripts(gl, ["vertex-shader-3d", "fragment-shader-3d"]);
// look up where the vertex data needs to go.
var positionLocation = gl.getAttribLocation(program, "a_position");
var colorLocation = gl.getAttribLocation(program, "a_color");
// lookup uniforms
var matrixLocation = gl.getUniformLocation(program, "u_matrix");
// Create a buffer to put positions in
var positionBuffer = gl.createBuffer();
// Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = positionBuffer)
gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
// Put geometry data into buffer
setGeometry(gl);
// Create a buffer to put colors in
var colorBuffer = gl.createBuffer();
// Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = colorBuffer)
gl.bindBuffer(gl.ARRAY_BUFFER, colorBuffer);
// Put geometry data into buffer
setColors(gl);
function radToDeg(r) {
return r * 180 / Math.PI;
}
function degToRad(d) {
return d * Math.PI / 180;
}
var translation = [45, 150, 0];
var rotation = [degToRad(40), degToRad(25), degToRad(325)];
var scale = [1, 1, 1];
drawScene();
// Setup a ui.
webglLessonsUI.setupSlider("#x", {value: translation[0], slide: updatePosition(0), max: gl.canvas.width });
webglLessonsUI.setupSlider("#y", {value: translation[1], slide: updatePosition(1), max: gl.canvas.height});
webglLessonsUI.setupSlider("#z", {value: translation[2], slide: updatePosition(2), max: gl.canvas.height});
webglLessonsUI.setupSlider("#angleX", {value: radToDeg(rotation[0]), slide: updateRotation(0), max: 360});
webglLessonsUI.setupSlider("#angleY", {value: radToDeg(rotation[1]), slide: updateRotation(1), max: 360});
webglLessonsUI.setupSlider("#angleZ", {value: radToDeg(rotation[2]), slide: updateRotation(2), max: 360});
webglLessonsUI.setupSlider("#scaleX", {value: scale[0], slide: updateScale(0), min: -5, max: 5, step: 0.01, precision: 2});
webglLessonsUI.setupSlider("#scaleY", {value: scale[1], slide: updateScale(1), min: -5, max: 5, step: 0.01, precision: 2});
webglLessonsUI.setupSlider("#scaleZ", {value: scale[2], slide: updateScale(2), min: -5, max: 5, step: 0.01, precision: 2});
function updatePosition(index) {
return function(event, ui) {
translation[index] = ui.value;
drawScene();
};
}
function updateRotation(index) {
return function(event, ui) {
var angleInDegrees = ui.value;
var angleInRadians = angleInDegrees * Math.PI / 180;
rotation[index] = angleInRadians;
drawScene();
};
}
function updateScale(index) {
return function(event, ui) {
scale[index] = 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.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
// Turn on culling. By default backfacing triangles
// will be culled.
// WebGL은 삼각형의 앞 뒷면을 그릴 수 있다. 앞면은 반시계 방향 버텍스, 뒷면은 시계 방향 버텍스 순서
// 이 옵션을 켜두면 삼각형이 뒤집혔을 때 뒷면이 보이지 않는다.
gl.enable(gl.CULL_FACE);
// Enable the depth buffer
gl.enable(gl.DEPTH_TEST);
// Tell it to use our program (pair of shaders)
gl.useProgram(program);
// Turn on the position attribute
gl.enableVertexAttribArray(positionLocation);
// Bind the position buffer.
gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
// Tell the position 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(
positionLocation, size, type, normalize, stride, offset);
// Turn on the color attribute
gl.enableVertexAttribArray(colorLocation);
// Bind the color buffer.
gl.bindBuffer(gl.ARRAY_BUFFER, colorBuffer);
// 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 values
var normalize = true; // normalize the data (convert from 0-255 to 0-1)
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(
colorLocation, size, type, normalize, stride, offset);
// Compute the matrices
var matrix = m4.projection(gl.canvas.clientWidth, gl.canvas.clientHeight, 400);
matrix = m4.translate(matrix, translation[0], translation[1], translation[2]);
matrix = m4.xRotate(matrix, rotation[0]);
matrix = m4.yRotate(matrix, rotation[1]);
matrix = m4.zRotate(matrix, rotation[2]);
matrix = m4.scale(matrix, scale[0], scale[1], scale[2]);
// Set the matrix.
gl.uniformMatrix4fv(matrixLocation, false, matrix);
// Draw the geometry.
var primitiveType = gl.TRIANGLES;
var offset = 0;
var count = 16 * 6;
gl.drawArrays(primitiveType, offset, count);
}
}
var m4 = {
projection: function(width, height, depth) {
// Note: This matrix flips the Y axis so 0 is at the top.
return [
2 / width, 0, 0, 0,
0, -2 / height, 0, 0,
0, 0, 2 / depth, 0,
-1, 1, 0, 1,
];
},
multiply: function(a, b) {
var a00 = a[0 * 4 + 0];
var a01 = a[0 * 4 + 1];
var a02 = a[0 * 4 + 2];
var a03 = a[0 * 4 + 3];
var a10 = a[1 * 4 + 0];
var a11 = a[1 * 4 + 1];
var a12 = a[1 * 4 + 2];
var a13 = a[1 * 4 + 3];
var a20 = a[2 * 4 + 0];
var a21 = a[2 * 4 + 1];
var a22 = a[2 * 4 + 2];
var a23 = a[2 * 4 + 3];
var a30 = a[3 * 4 + 0];
var a31 = a[3 * 4 + 1];
var a32 = a[3 * 4 + 2];
var a33 = a[3 * 4 + 3];
var b00 = b[0 * 4 + 0];
var b01 = b[0 * 4 + 1];
var b02 = b[0 * 4 + 2];
var b03 = b[0 * 4 + 3];
var b10 = b[1 * 4 + 0];
var b11 = b[1 * 4 + 1];
var b12 = b[1 * 4 + 2];
var b13 = b[1 * 4 + 3];
var b20 = b[2 * 4 + 0];
var b21 = b[2 * 4 + 1];
var b22 = b[2 * 4 + 2];
var b23 = b[2 * 4 + 3];
var b30 = b[3 * 4 + 0];
var b31 = b[3 * 4 + 1];
var b32 = b[3 * 4 + 2];
var b33 = b[3 * 4 + 3];
return [
b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30,
b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31,
b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32,
b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33,
b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30,
b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31,
b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32,
b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33,
b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30,
b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31,
b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32,
b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33,
b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30,
b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31,
b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32,
b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33,
];
},
translation: function(tx, ty, tz) {
return [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
tx, ty, tz, 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));
},
};
// Fill the 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 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);
}
main();
Perspective
원근감이 있는 3D
-WebGL은 vertex shader의 gl_Position에 할당한 x,y,z,w 값을 가져와 자동으로 w로 나눈다.
1.
function makeZToWMatrix(fudgeFactor) {
return [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, fudgeFactor,
0, 0, 0, 1,
];
}
var m4 = {
perspective: function(fieldOfViewInRadians, aspect, near, far) {
var f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewInRadians);
var rangeInv = 1.0 / (near - far);
return [
f / aspect, 0, 0, 0,
0, f, 0, 0,
0, 0, (near + far) * rangeInv, -1,
0, 0, near * far * rangeInv * 2, 0
];
},
...
}
Cameras
카메라를 회전하는법
- 절두체를 중심으로 inverse matrices를 이용한 카메라 회전 - inverse
- 카메라 위치와 타겟점을 이용한 회전 - lookAt
"use strict";
function main() {
// Get A WebGL context
/** @type {HTMLCanvasElement} */
var canvas = document.querySelector("#canvas");
var gl = canvas.getContext("webgl");
if (!gl) {
return;
}
// setup GLSL program
var program = webglUtils.createProgramFromScripts(gl, ["vertex-shader-3d", "fragment-shader-3d"]);
// look up where the vertex data needs to go.
var positionLocation = gl.getAttribLocation(program, "a_position");
var colorLocation = gl.getAttribLocation(program, "a_color");
// lookup uniforms
var matrixLocation = gl.getUniformLocation(program, "u_matrix");
// Create a buffer to put positions in
var positionBuffer = gl.createBuffer();
// Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = positionBuffer)
gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
// Put geometry data into buffer
setGeometry(gl);
// Create a buffer to put colors in
var colorBuffer = gl.createBuffer();
// Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = colorBuffer)
gl.bindBuffer(gl.ARRAY_BUFFER, colorBuffer);
// Put color data into buffer
setColors(gl);
function radToDeg(r) {
return r * 180 / Math.PI;
}
function degToRad(d) {
return d * Math.PI / 180;
}
var cameraAngleRadians = degToRad(0);
var fieldOfViewRadians = degToRad(60);
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 AND the depth buffer.
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
// Turn on culling. By default backfacing triangles
// will be culled.
gl.enable(gl.CULL_FACE);
// Enable the depth buffer
gl.enable(gl.DEPTH_TEST);
// Tell it to use our program (pair of shaders)
gl.useProgram(program);
// Turn on the position attribute
gl.enableVertexAttribArray(positionLocation);
// Bind the position buffer.
gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
// Tell the position 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(
positionLocation, size, type, normalize, stride, offset);
// Turn on the color attribute
gl.enableVertexAttribArray(colorLocation);
// Bind the color buffer.
gl.bindBuffer(gl.ARRAY_BUFFER, colorBuffer);
// 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 values
var normalize = true; // normalize the data (convert from 0-255 to 0-1)
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(
colorLocation, size, type, normalize, stride, offset);
var numFs = 5;
var radius = 200;
// Compute the projection matrix
var aspect = gl.canvas.clientWidth / gl.canvas.clientHeight;
var zNear = 1;
var zFar = 2000;
var projectionMatrix = m4.perspective(fieldOfViewRadians, aspect, zNear, zFar);
// Compute the position of the first F
var fPosition = [radius, 0, 0];
// Use matrix math to compute a position on a circle where
// the camera is
var cameraMatrix = m4.yRotation(cameraAngleRadians);
cameraMatrix = m4.translate(cameraMatrix, 0, 0, radius * 1.5);
// Get the camera's position from the matrix we computed
var cameraPosition = [
cameraMatrix[12],
cameraMatrix[13],
cameraMatrix[14],
];
var up = [0, 1, 0];
// Compute the camera's matrix using look at.
var cameraMatrix = m4.lookAt(cameraPosition, fPosition, up);
// Make a view matrix from the camera matrix
var viewMatrix = m4.inverse(cameraMatrix);
// Compute a view projection matrix
var viewProjectionMatrix = m4.multiply(projectionMatrix, viewMatrix);
for (var ii = 0; ii < numFs; ++ii) {
var angle = ii * Math.PI * 2 / numFs;
var x = Math.cos(angle) * radius;
var y = Math.sin(angle) * radius;
// starting with the view projection matrix
// compute a matrix for the F
var matrix = m4.translate(viewProjectionMatrix, x, 0, y);
// Set the matrix.
gl.uniformMatrix4fv(matrixLocation, false, matrix);
// Draw the geometry.
var primitiveType = gl.TRIANGLES;
var offset = 0;
var count = 16 * 6;
gl.drawArrays(primitiveType, offset, count);
}
}
}
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];
}
}
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]];
}
var m4 = {
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], xAxis[1], xAxis[2], 0,
yAxis[0], yAxis[1], yAxis[2], 0,
zAxis[0], zAxis[1], zAxis[2], 0,
cameraPosition[0],
cameraPosition[1],
cameraPosition[2],
1,
];
},
perspective: function(fieldOfViewInRadians, aspect, near, far) {
var f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewInRadians);
var rangeInv = 1.0 / (near - far);
return [
f / aspect, 0, 0, 0,
0, f, 0, 0,
0, 0, (near + far) * rangeInv, -1,
0, 0, near * far * rangeInv * 2, 0
];
},
projection: function(width, height, depth) {
// Note: This matrix flips the Y axis so 0 is at the top.
return [
2 / width, 0, 0, 0,
0, -2 / height, 0, 0,
0, 0, 2 / depth, 0,
-1, 1, 0, 1,
];
},
multiply: function(a, b) {
var a00 = a[0 * 4 + 0];
var a01 = a[0 * 4 + 1];
var a02 = a[0 * 4 + 2];
var a03 = a[0 * 4 + 3];
var a10 = a[1 * 4 + 0];
var a11 = a[1 * 4 + 1];
var a12 = a[1 * 4 + 2];
var a13 = a[1 * 4 + 3];
var a20 = a[2 * 4 + 0];
var a21 = a[2 * 4 + 1];
var a22 = a[2 * 4 + 2];
var a23 = a[2 * 4 + 3];
var a30 = a[3 * 4 + 0];
var a31 = a[3 * 4 + 1];
var a32 = a[3 * 4 + 2];
var a33 = a[3 * 4 + 3];
var b00 = b[0 * 4 + 0];
var b01 = b[0 * 4 + 1];
var b02 = b[0 * 4 + 2];
var b03 = b[0 * 4 + 3];
var b10 = b[1 * 4 + 0];
var b11 = b[1 * 4 + 1];
var b12 = b[1 * 4 + 2];
var b13 = b[1 * 4 + 3];
var b20 = b[2 * 4 + 0];
var b21 = b[2 * 4 + 1];
var b22 = b[2 * 4 + 2];
var b23 = b[2 * 4 + 3];
var b30 = b[3 * 4 + 0];
var b31 = b[3 * 4 + 1];
var b32 = b[3 * 4 + 2];
var b33 = b[3 * 4 + 3];
return [
b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30,
b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31,
b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32,
b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33,
b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30,
b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31,
b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32,
b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33,
b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30,
b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31,
b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32,
b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33,
b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30,
b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31,
b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32,
b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33,
];
},
translation: function(tx, ty, tz) {
return [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
tx, ty, tz, 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));
},
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))
];
},
vectorMultiply: function(v, m) {
var dst = [];
for (var i = 0; i < 4; ++i) {
dst[i] = 0.0;
for (var j = 0; j < 4; ++j) {
dst[i] += v[j] * m[j * 4 + i];
}
}
return dst;
},
};
// Fill the buffer with the values that define a letter 'F'.
function setGeometry(gl) {
var positions = 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]);
// Center the F around the origin and Flip it around. We do this because
// we're in 3D now with and +Y is up where as before when we started with 2D
// we had +Y as down.
// We could do by changing all the values above but I'm lazy.
// We could also do it with a matrix at draw time but you should
// never do stuff at draw time if you can do it at init time.
var matrix = m4.xRotation(Math.PI);
matrix = m4.translate(matrix, -50, -75, -15);
for (var ii = 0; ii < positions.length; ii += 3) {
var vector = m4.vectorMultiply([positions[ii + 0], positions[ii + 1], positions[ii + 2], 1], matrix);
positions[ii + 0] = vector[0];
positions[ii + 1] = vector[1];
positions[ii + 2] = vector[2];
}
gl.bufferData(gl.ARRAY_BUFFER, positions, gl.STATIC_DRAW);
}
// Fill the 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);
}
main();
출처
https://webglfundamentals.org/webgl/lessons/ko/webgl-3d-orthographic.html
https://webglfundamentals.org/webgl/lessons/ko/webgl-3d-perspective.html
https://webglfundamentals.org/webgl/lessons/webgl-3d-camera.html