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2021-08-21 20:45:29 +02:00 · 2021-08-21 20:45:29 +02:00 · 03fe1df64b
commit 03fe1df64b
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--- a/app/Understanding
+++ b/app/Understanding
--- a/images/0.png
+++ b/images/0.png
--- a/images/1.png
+++ b/images/1.png
--- a/images/1d.png
+++ b/images/1d.png
--- a/images/2.png
+++ b/images/2.png
--- a/images/3.png
+++ b/images/3.png
--- a/images/3d.png
+++ b/images/3d.png
--- a/images/3d.png~
+++ b/images/3d.png~
--- a/images/4.png
+++ b/images/4.png
--- a/images/4d.png
+++ b/images/4d.png
--- a/images/4d.png~
+++ b/images/4d.png~
--- a/images/5.png
+++ b/images/5.png
--- a/images/anglesToRotate.png
+++ b/images/anglesToRotate.png
--- a/images/basicRotations.png
+++ b/images/basicRotations.png
--- a/images/colorVisualizationFor2D.png
+++ b/images/colorVisualizationFor2D.png
--- a/images/colorVisualizationFor2D.png~
+++ b/images/colorVisualizationFor2D.png~
--- a/images/colorVisualizationForW.png
+++ b/images/colorVisualizationForW.png
--- a/images/colorVisualizationForW.png~
+++ b/images/colorVisualizationForW.png~
--- a/images/directionalLightAndAmbientLightGradient.png
+++ b/images/directionalLightAndAmbientLightGradient.png
--- a/images/halfDonutVisualizedIn2D.png
+++ b/images/halfDonutVisualizedIn2D.png
--- a/images/heightmap.png
+++ b/images/heightmap.png
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/images/images
+++ b/images/images
--- a/app/main0.png
+++ b/app/main0.png
--- a/app/main1.png
+++ b/app/main1.png
--- a/app/main1_.png
+++ b/app/main1_.png
--- a/rotations.png
+++ b/rotations.png
--- a/images/knownRotations2D.png
+++ b/images/knownRotations2D.png
--- a/images/main.png
+++ b/images/main.png
--- a/images/newRotations.png
+++ b/images/newRotations.png
--- a/images/projected3Ddonut.png
+++ b/images/projected3Ddonut.png
--- a/images/projectingTwiceFrom3D.png
+++ b/images/projectingTwiceFrom3D.png
--- a/images/projectingTwiceFrom4D.png
+++ b/images/projectingTwiceFrom4D.png
--- a/images/unknownRotationOnDonut.png
+++ b/images/unknownRotationOnDonut.png
--- a/images/unknownRotationsUsedForCreatingObjects.png
+++ b/images/unknownRotationsUsedForCreatingObjects.png
--- a/index.html
+++ b/index.html
@ -0,0 +1,315 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
    <meta charset="UTF-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <link rel="stylesheet" type="text/css" href="styles/style.css"/>
    <script src="libraries/jquery-3.6.0.min.js"></script>
    <title>Understanding 4D</title>
 </head>
 <body>
    <header>
        <nav></nav>
    </header>
    <p class="title"><strong>Understanding 4D</strong></p>
    <div class="a">
        <span class="highlight_text">0. Introduction</span> <br/>
        <p class="normal_text mtop">
            Hello, I am Tucan. <br/>
            In this course I will be explaining some ways of how to
            think about 4D and then explain rotations of a 4D object that kinda looks like a donut. There will be a lot of interactive stuff so look forward to that. <br/>
            Intuition is all you'll need.
        </p>
    </div>
    <div class="a">
        <p class="normal_text">
            Also please download
            <a href="./desktop app/Understanding 4D.zip" class="normal_text" download>this application.</a>  
            (<a href="https://drive.google.com/file/d/1iRUxC5VLrMRLLMBHvf7_ZTHKjQovYyPa/view?usp=sharing" class="normal_text" download>source code</a>)<br/>
            It contains several scenes that will be useful in our explanation. <br/>
            You can continue without the app if you want to. <br/>
            There will be screenshots of the scenes, but they won't be interactive.
        </p>
    </div>
    <div class="a">
        <span class="highlight_text">1. What are we going to see?</span>
        <p class="normal_text mtop">
            Before we look at 4D and try understanding it, we need to know what are we going to be seeing and how. <br/>
            To answer that, first let's look at what person in 1D would see.
        </p>
        <img src="./images/1d.png" class="normal_image"/>
        <p class="normal_text mtop">
            Person in 1D would see 1 piece of information or 0D.  <br/>
            Now let's look what happens in 2D. (use slider to move the points around)
        </p>
        <canvas class="c" width=1100px height=360px></canvas>
        <p class="normal_text mtop">
            As we saw above person in 2D would see a line or section of 1D. <br/>
            Let's continue to 3D.
        </p>
        <img src="./images/3d.png" class="normal_image"/>
        <p class="normal_text mtop">
            In 3D we see section of 2D. As shown on the image, by projecting onto 2D surface we get rid of z coordinates. <br/>
            Now let's look what would a person in 4D see.
        </p>
        <img src="./images/4d.png" class="normal_image"/>
        <p class="normal_text mtop">
            Every time we had person in some dimension what he saw was section of lower dimension. <br/>
            For example we live in 3D but see 2D. Similarly, a person in 4D would see 3D. <br/>
            But we can't see 3D space like person in 4D. <br/>
            For us, we need to project again, 3D => 2D. <br/>
            Then we can see 2D section that we end up with.<br/>
            Let me give you example of projecting twice. 3D => 2D => 1D
        </p>
        <img src="./images/projectingTwiceFrom3D.png" class="normal_image"/>
        <p class="normal_text mtop">
            Now, let's move onto our case 4D => 3D => 2D.
            We'll ignore 4D person for less confusion.
        </p>
        <img src="./images/projectingTwiceFrom4D.png" class="normal_image"/>
        <p class="normal_text mtop">
            By projecting twice we get something that we can see. <br/>
        </p>
    </div>
    <div class="a">
        <span class="highlight_text">2. Visualizing w axis using color</span>
        <p class="normal_text mtop">
            Before we do w axis let's try visualizing z axis with color in 2D. <br/>
            To do that we can use heightmaps. In heightmaps color is used to indicate height.<br/>
            Below we have 3D surface on the left and its heightmap on the right. <br/>
        </p>
        <div class="row">
            <video width="854" height="480" controls class="normal_video">
                <source src="./videos/Terrain3D.mp4" type="video/mp4">
            </video>
            <img src="./images/heightmap.png" class="normal_image"/>
        </div>
        <p class="normal_text mtop">
            Using only black and white can be problematic with negative values. <br/>
            By using more colors we can get more information from looking at heightmaps. <br/>
            Let's use blue and green.
        </p>
        <img src="./images/colorVisualizationFor2D.png" class="normal_image"/>
        <p class="normal_text mtop">
            We can also use this to visualize the w axis.
        </p>
        <img src="./images/colorVisualizationForW.png" class="normal_image"/>
    </div>
    <div class="a">
        <span class="highlight_text">3. Creating 4D object</span>
        <p class="normal_text mtop">
            Now it's going to start getting exciting. <br/>
            4D object that we're going to create is in some ways similar to donut. <br/>
            That's why we will look at how to create a donut first. <br/>
            We can create a donut by rotating circle around a line. <br/>
            Below is how it would look in 2D visualized by color. <br/>
            Note that object below is only half donut. (sigle color per circle used for simplicity) <br/>
        </p>
        <img src="./images/halfDonutVisualizedIn2D.png" class="normal_image"/>
        <p class="normal_text mtop">
            As we saw above 2D person would see a circle that's getting squashed and its color changes. <br/>
            We're going to create our 4D object similarly but use spheres instead and rotate into the 4th dimension. <br/>
            Before that let's look at what we need to do basic rotations. <br/>
            All we need for basic rotation are 2 variables forming a plane. <br/>
            Its nicely demonstrated on the image below.
        </p>
        <img src="./images/basicRotations.png" class="normal_image"/>
        <p class="normal_text mtop">
            Now we can start creating our 4D object. <br/>
            Were going to do something similar to making a donut from circle. <br/>
            But instead of circles were going to use spheres, and rotate into 4D using rotation with x and w. <br/>
            Explore 3D scene that's illustrating half of the rotation. (signle color per sphere used for simplicity)
        </p>
        <iframe src="./spline scenes/4_d_donut_creation/index.html" frameborder=0 class="spline_scene"></iframe>
        <p class="normal_text mtop">
            Now let's go back to normal donut. <br/>
            What would a person in 2D see when we project the donut. <br/>
            We count that the donut was created using method above and not manipulated yet.
        </p>
        <img src="./images/projected3Ddonut.png" class="normal_image"/>
        <p class="normal_text mtop">
            When person that's in 2D saw that projected donut, <br/>
            it looked something like rectangle with rounded corners. <br/>
            Because we created our 4D object using similar method we can use this. <br/>
            If this scales nicely, we should see something like cuboid (stretched cube) with rounded corners. <br/>
            Please open the desktop app mentioned at the begging. <br/>
            Then click on the button shown below to run projection of 4D object. (in app)
        </p>
        <img src="./images/0.png" class="normal_image"/>
        <img src="./images/images from desktop app/0.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            As we saw, it looked like cuboid with rounded corners.
        </p>
    </div>
    <div class="a">
        <span class="highlight_text">4. Exploring 4D object</span>
        <p class="normal_text mtop">
            There are a lot of confusing things that can happen when we rotate higher dimensional objects. <br/>
            So to get a little less confused we're going to look at rotations and their behavior first. <br/>
            Below is table with dimensions and rotations that become possible in that dimension.
        </p>
        <img src="./images/newRotations.png" class="normal_image"/>
        <p class="normal_text mtop">
            Now let's split rotations into known and unknown. <br/>
            Known rotations will be those that exist in our dimension. <br/>
            And unknown rotations will be those that are in higher dimensions. <br/>
            The number of unknown rotations will always be infinite like the number of higher dimensions. <br/>
            For example, if we're in 2D we have 1 known rotation.
        </p>
        <img src="./images/known and unknown rotations.png" class="normal_image"/>
        <p class="normal_text mtop">
            Using known rotations on higher dimensional objects doesn't change the behavior of known rotations. <br/>
            For example, if we're in 2D and use known rotation on 3D donut it would rotate like we would expect.
        </p>
        <img src="./images/knownRotations2D.png" class="normal_image"/>
        <p class="normal_text mtop">
             Also in the first scene that we used app to run were only known rotations inplace. <br/>
             That's why you haven't seen any unusual motion. <br/>
             To create higher dimensional objects in some dimension we used unknown rotations. <br/>
             Let's look again at where we used them.
        </p>
        <img src="./images/unknownRotationsUsedForCreatingObjects.png" class="normal_image"/>
        <p class="normal_text mtop">
            Now we will use these unknown rotations to rotate the objects.  <br/>
            We're going to start with normal donut. <br/>
            For person in 2D it looks as if the points are cycling through the object.
        </p>
        <img src="./images/unknownRotationOnDonut.png" class="normal_image"/>
        <p class="normal_text mtop">
            Next we're going to do the same with our 4D object. <br/>
            Click the button shown below. (in app)
        </p>
        <img src="./images/5.png" class="normal_image"/>
        <img src="./images/images from desktop app/5.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            Another thing we can do is use reverse rendering. <br/>
            Here, that means seeing whats furthest away first. <br/>
            This way we can see more useful information. <br/>
            Let's start with rendering normal 3D donut with reverse. <br/>
            Click the button shown below. (in app)
        </p>
        <img src="./images/1.png" class="normal_image"/>
        <img src="./images/images from desktop app/1.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            Using reverse we could see the backside and partially see front side as well when they overlapped. <br/>
            Next were going to use reverse with our 4D object. <br/>
            Click the button shown below. (in app)
        </p>
        <img src="./images/2.png" class="normal_image"/>
        <img src="./images/images from desktop app/2.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            Next we'll change lighting. <br/>
            Instead of normal lighting we can use ambient light gradients (alg). <br/>
            With them we can get better sense of distance. <br/>
            Image below is showing difference between directional lighting and alg.
        </p>
        <img src="./images/directionalLightAndAmbientLightGradient.png" class="normal_image"/>
        <p class="normal_text mtop">
            Actually alg that's used in the app is a little different to improve performance. <br/>
            But it still looks similar enough. <br/>
            Now we'll try alg with 3D donut. <br/>
            Click the button shown below. (in app)
        </p>
        <img src="./images/3.png" class="normal_image"/>
        <img src="./images/images from desktop app/3.png" class="normal_image mleft"/>
        <img src="./images/images from desktop app/3_.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            Let's continue with our 4D object. <br/>
            Click the button shown below. (in app)
        </p>
        <img src="./images/4.png" class="normal_image"/>
        <img src="./images/images from desktop app/4.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            There's one more thing we will do in this explanation. <br/>
            We never combined known and unknown rotations together with our 4D object. <br/>
            Because of that we never got to see all states of our 4D object. <br/>
            To access all rotated states of 4D object we need 3 angles. <br/>
            Below image illustrates this.
        </p>
        <img src="./images/anglesToRotate.png" class="normal_image"/>
        <p class="normal_text mtop">
            Now, let's try it with our 4D object. <br/>
            Click the button shown below. (in app)
        </p>
        <img src="./images/main.png" class="normal_image"/>
        <img src="./images/images from desktop app/main0.png" class="normal_image mleft"/>
        <img src="./images/images from desktop app/main1.png" class="normal_image mleft"/>
        <img src="./images/images from desktop app/main1_.png" class="normal_image mleft"/>
        <p class="normal_text mtop">
            And with that, here ends the explanation. <br/> <br/>
            <a href="https://github.com/Tucan444/Understanding-4D" class="normal_text">Github<a/>
        </p>
    </div>
    <script src="scripts/2Dprojection.js"></script>
 </body>
 </html>
--- a/libraries/jquery-3.6.0.min.js
+++ b/libraries/jquery-3.6.0.min.js
--- a/scripts/2Dprojection.js
+++ b/scripts/2Dprojection.js
@ -0,0 +1,333 @@
 function rgb_to_hex(r, g, b) {
    r = Math.round(r).toString(16);
    g = Math.round(g).toString(16);
    b = Math.round(b).toString(16);
    if (r.length < 2) {
        r = "0" + r;
    }
    if (g.length < 2) {
        g = "0" + g;
    }
    if (b.length < 2) {
        b = "0" + b;
    }
    return `#${r}${g}${b}`;
 }
 class RotatingPoint2D {
    constructor(x, y, theta, magnitude, size, color) {
        this.x = x;
        this.y = y;
        // r as rotated
        this.rx = x;
        this.ry = y;
        this.theta = theta;
        this.magnitude = magnitude;
        this.size = size;
        this.color = color;
        this.shaded_color = [0, 0, 0];
        this.d = 0;
        this.linewidth = 4;
        this.offset = [400, 180];
        this.TAU = Math.PI * 2;
    }
    shade = function(light_x, light_y, light_intensity) {
        let differences = [this.rx - light_x, this.ry - light_y];
        let distance = Math.sqrt(Math.pow(differences[0], 2) + Math.pow(differences[1], 2));
        let alpha = Math.max(0, -(distance - light_intensity) / light_intensity);
        this.shaded_color = [this.color[0] * alpha, this.color[1] * alpha, this.color[2] * alpha];
    }
    rotate = function(alpha = 0) {
        let beta = alpha + this.theta;
        this.rx = Math.cos(beta) * this.magnitude;
        this.ry = Math.sin(beta) * this.magnitude;
    }
    find_d = function(player_pos) {
        let offseted_player_pos = [player_pos[0] - this.offset[0], player_pos[1] - this.offset[1]];
        let differences = [this.rx - offseted_player_pos[0], this.ry - offseted_player_pos[1]];
        this.d = Math.pow(differences[0], 2) + Math.pow(differences[1], 2);
    }
    draw_line_to_player = function(ctx, player_pos) {
        ctx.beginPath();
        ctx.strokeStyle = rgb_to_hex(this.shaded_color[0], this.shaded_color[1], this.shaded_color[2]);
        ctx.lineWidth = this.linewidth;
        ctx.moveTo(this.rx + this.offset[0], this.ry + this.offset[1])
        ctx.lineTo(player_pos[0], player_pos[1]);
        ctx.stroke();
    }
    blit = function(ctx) {
        ctx.beginPath();
        ctx.fillStyle = rgb_to_hex(this.shaded_color[0], this.shaded_color[1], this.shaded_color[2]);
        ctx.arc(this.rx + this.offset[0], this.ry + this.offset[1], this.size, 0, this.TAU);
        ctx.fill();
    }
    get_projected_positions = function(player_pos, projection_size, canvas_height) {
        let player_pos_x = player_pos[0] - this.offset[0];
        let projected_pos = this.ry * (projection_size[0] / (player_pos_x - this.rx)) * (canvas_height / projection_size[1]);
        return projected_pos + player_pos[1];
    }
 }
 class VerticalSliderPoint {
    constructor (x, y, r, colors, constrains) {
        this.x = x;
        this.y = y;
        this.r = r;
        this.colors = colors;  // 0 for idle 1 for hover 2 for active
        this.constrains = constrains;
        this.TAU = Math.PI * 2;
    }
    set_y = function(y) {
        if (y < this.constrains[0]) {
            this.y = this.constrains[0];
        } else if (y > this.constrains[1]) {
            this.y = this.constrains[1];
        } else {
            this.y = y;
        }
    }
    collidepoint = function (x, y) {
        let differences = [this.x - x, this.y - y];
        let distance = Math.sqrt(Math.pow(differences[0], 2) + Math.pow(differences[1], 2));
        return (distance <= this.r);
    }
    get_progress = function() {
        let progress = this.y - this.constrains[0];
        progress /= this.constrains[1] - this.constrains[0];
        return progress;
    }
    blit = function(ctx, color_index) {
        ctx.beginPath();
        ctx.lineWidth = 1;
        ctx.fillStyle = this.colors[color_index];
        ctx.arc(this.x, this.y, this.r, 0, this.TAU);
        ctx.fill();
    }
 }
 console.log("a");
 $(document).ready(function(){
    console.log("b");
    let c = $(".c")[0];
    let ctx = c.getContext("2d");
    let TAU = Math.PI * 2;
    let canvas_size = [1100, 360];
    let view_width = 120;
    let thin_line_width = 6;
    let normal_line_width = 20;
    let alpha = 0;
    let mousedown = false;
    let on_slider = false;
    let player_pos = [canvas_size[0] - 360, canvas_size[1] /2];
    let projection_size = [100, 120];
    let slider_padding_top_bottom = 40;
    let slider_angle = TAU * 1.2;
    let creamy_white = "#c3c3c3";
    let creamy_gray_light = "#a3a3a3"
    let creamy_gray = "#999999";
    let creamy_gray_dark = "#777777";
    let green = "#6de256";
    let sliderMode = 0;
    let sliderPoint = new VerticalSliderPoint(50, slider_padding_top_bottom, 16,
                                              [creamy_gray, creamy_gray_light, creamy_white],
                                              [slider_padding_top_bottom, canvas_size[1] - slider_padding_top_bottom]);
    let points = [new RotatingPoint2D(60, 0, 0, 60, 20, [255, 100, 100]),
                  new RotatingPoint2D(Math.cos((Math.PI / 3) * 2) * 80, Math.sin((Math.PI / 3) * 2) * 80, (Math.PI / 3) * 2, 80, 20, [255, 100, 100]),
                  new RotatingPoint2D(Math.cos((Math.PI / 3) * 4) * 110, Math.sin((Math.PI / 3) * 4) * 110, (Math.PI / 3) * 4, 110, 20, [255, 100, 100])];
    for (let i = 0; i < points.length; i++) {
        points[i].shade(100, 100, 400);
        points[i].find_d(player_pos);
        points[i].draw_line_to_player(ctx, player_pos);
    }
    points.sort((a, b) => (a.d < b.d) ? 1 : -1);
    draw_projected_view();
    draw_static_objects();
    sliderPoint.blit(ctx, 0);
    for(let i = 0; i<points.length; i++) {
        points[i].blit(ctx);
    }
    function draw_static_objects() {
        ctx.beginPath();
        ctx.strokeStyle = creamy_white;
        ctx.lineWidth = normal_line_width;
        ctx.moveTo(canvas_size[0] - view_width, 0);
        ctx.lineTo(canvas_size[0] - view_width, canvas_size[1])
        ctx.stroke();
        ctx.beginPath();
        ctx.strokeStyle = creamy_gray_dark;
        ctx.lineWidth = thin_line_width;
        ctx.moveTo(50, slider_padding_top_bottom);
        ctx.lineTo(50, canvas_size[1] - slider_padding_top_bottom);
        ctx.stroke();
        ctx.beginPath();
        ctx.strokeStyle = creamy_white;
        ctx.moveTo(player_pos[0], player_pos[1]);
        ctx.lineTo(player_pos[0] - projection_size[0], player_pos[1] - (projection_size[1] / 2));
        ctx.lineTo(player_pos[0] - projection_size[0], player_pos[1] + (projection_size[1] / 2));
        ctx.lineTo(player_pos[0], player_pos[1]);
        ctx.stroke();
        ctx.beginPath();
        ctx.fillStyle = green;
        ctx.arc(player_pos[0], player_pos[1], 20, 0, TAU);
        ctx.fill();
    }
    function draw_projected_view() {
        ctx.lineWidth = normal_line_width;
        for (var i = 0; i < points.length; ++i) {
            ctx.beginPath();
            ctx.strokeStyle = rgb_to_hex(points[i].shaded_color[0], points[i].shaded_color[1], points[i].shaded_color[2]);
            let projected_pos = points[i].get_projected_positions(player_pos, projection_size, canvas_size[1]);
            ctx.moveTo(canvas_size[0] - view_width, projected_pos);
            ctx.lineTo(canvas_size[0], projected_pos);
            ctx.stroke();
        }
    }
    function clear_canvas () {
        ctx.beginPath();
        ctx.fillStyle = "#282828";
        ctx.fillRect(0, 0, canvas_size[0], canvas_size[1]);
    }
    function draw_all () {
        clear_canvas();
        for (let i = 0; i < points.length; i++) {
            points[i].rotate(alpha);
            points[i].shade(100, 100, 400);
            points[i].find_d(player_pos);
            points[i].draw_line_to_player(ctx, player_pos);
        }
        points.sort((a, b) => (a.d < b.d) ? 1 : -1);
        draw_projected_view();
        draw_static_objects();
        sliderPoint.blit(ctx, sliderMode);
        for(let i = 0; i<points.length; i++) {
            points[i].blit(ctx);
        }
    }
    $(".c").mousemove(function(event){
        let mouse_pos = get_mouse_pos(event);
        if (mousedown && on_slider) {
            sliderMode = 2;
            sliderPoint.set_y(mouse_pos[1]);
            console.log(sliderPoint.y);
            alpha = slider_angle * sliderPoint.get_progress();
        } else if (sliderPoint.collidepoint(mouse_pos[0], mouse_pos[1])) {
            sliderMode = 1;
        } else {
            sliderMode = 0;
        }
        draw_all();
    });
    $(".c").mousedown(function(event){
        let mouse_pos = get_mouse_pos(event);
        mousedown = true;
        if (sliderPoint.collidepoint(mouse_pos[0], mouse_pos[1])) {
            on_slider = true;
            sliderMode = 2;
            draw_all();
        }
    });
    $("body").mouseup(function(event) {
        let mouse_pos = get_mouse_pos(event);
        mousedown = false;
        if (on_slider) {
            on_slider = false;
            sliderMode = 1 * sliderPoint.collidepoint(mouse_pos[0], mouse_pos[1]);
            draw_all();
        }
    });
    // other functions
    function get_mouse_pos(event) {
        let rect = c.getBoundingClientRect();
        return [event.clientX - rect.left, event.clientY - rect.top];
    }
 });
--- a/scenes/4_d_donut_creation/index.html
+++ b/scenes/4_d_donut_creation/index.html
@ -0,0 +1,57 @@
         <!DOCTYPE html>
         <html lang="en">
             <head>
                 <meta charset="UTF-8">
                 <meta name="viewport" content="width=device-width, initial-scale=1.0">
                 <style>
                     body { width: 100%;
                            height: 100%;
                            margin: 0;
                            position: fixed;
                            background: rgba(25,25,25, 1) }
                     canvas { width: 100%; height: 100%; outline: none; }
                     #container { width: 100%; height: 100%; position: relative; }
                     .spline-watermark {
                         position: absolute;
                         bottom: 16px;
                         right: 16px;
                         width: 32px;
                         height: 32px;
                         z-index: 2;
                     }
                     .spline-watermark:hover {
                         opacity: 0.8;
                     }
                     .spline-watermark img {
                         display: block;
                         width: 100%;
                         height: 100%;
                     }
                 </style>
                 <title>4D donut creation</title>
                 <link rel="icon" type="image/png" href="https://spline.design/_assets/_images/icon_favicon16x16.png" sizes="16x16">
                 <link rel="icon" type="image/png" href="https://spline.design/_assets/_images/icon_favicon32x32.png" sizes="32x32">
             </head>
             <body>
                 <div id='container'>
                     <canvas id="canvas3d"></canvas>
                     <a class="spline-watermark" href="https://spline.design">
                         <img src="https://spline.design/_assets/_images/icon_favicon32x32.png">
                     </a>
                 </div>
                 <script src="https://unpkg.com/three@0.131.3/build/three.min.js"></script>
                 <script src="js/spline.runtime.min.js"></script>
                 <script src="js/main.js"></script>
             </body>
         </html>
--- a/scenes/4_d_donut_creation/js/main.js
+++ b/scenes/4_d_donut_creation/js/main.js
@ -0,0 +1,4 @@
             const app = new SpeRuntime.Application();
             app.start('./scene.json');
--- a/scenes/4_d_donut_creation/js/spline.runtime.min.js
+++ b/scenes/4_d_donut_creation/js/spline.runtime.min.js
--- a/scenes/4_d_donut_creation/scene.json
+++ b/scenes/4_d_donut_creation/scene.json
--- a/styles/_classes.sass
+++ b/styles/_classes.sass
@ -0,0 +1,55 @@
@import ./_variables
@import ./_mixins
 .title
    text-align: center
    margin-top: 2%
    margin-bottom: 2%
    font-size: 60px
    width: 100%
    color: $text_color_0
 .a 
    margin: 0% 5% 5% 5%
    padding: 2%
    border-radius: 10px
    background-color: $primary_light 
    box-shadow:: 5px 5px 12px #141414
 .normal_text
    @include normal_text
    background-color: $primary_light
 .highlight_text
    @include highlight_text
    background-color: $primary_light
 .mtop
    margin-top: $mtop
 .mleft
    margin-left: $mleft
 .normal_image
    margin-top: $mtop + $image_margins_size
    margin-bottom: $image_margins_size
    box-shadow: 10px 10px 24px #111
 .normal_video
    margin-top: $mtop + $video_margins_size
    margin-bottom: $video_margins_size
    box-shadow: 10px 10px 24px #111
 .row
    margin-top: $mtop
    display: flex
    justify-content: space-around
    flex-direction: row
    border-radius: 10px
 .spline_scene
    margin-top: $mtop + $spline_scene_margins_size
    margin-bottom: $spline_scene_margins_size
    box-shadow: 10px 10px 24px #111
    width: 1000px
    height: 600px
--- a/styles/_main_tags.sass
+++ b/styles/_main_tags.sass
@ -0,0 +1,12 @@
@import ./_variables
 nav
    width: 100%
    height: 30px
    box-shadow: 0px 0px 20px #000
    background-color: $primary_dark
 canvas
    margin-top: $mtop + $canvas_margins_size
    margin-bottom: $canvas_margins_size
    box-shadow: 10px 10px 24px #111
--- a/styles/_mixins.sass
+++ b/styles/_mixins.sass
@ -0,0 +1,21 @@
@import ./_variables
@mixin smaller_text
    font-size: $smaller_text_font_size
    color: text_color_0
    font-family: Arial, Helvetica, sans-ser
    letter-spacing: 0.6px
@mixin normal_text
    font-size: $normal_text_font_size
    color: $text_color_0
    font-family: Arial, Helvetica, sans-ser
    letter-spacing: 2px
@mixin highlight_text
    font-size: $highlight_text_font_size
    color: $text_color_1
    font-family: Arial, Helvetica, sans-serif
    letter-spacing: 1px
--- a/styles/_variables.sass
+++ b/styles/_variables.sass
@ -0,0 +1,19 @@
 $primary: #282828
 $primary_dark: #895d5d
 $primary_light: #313131
 $scrollbar_track_color: #373737
 $scrollbar_thumb_color: #4b4b4b
 $text_color_0: #d2d2d2
 $text_color_1: #e3e3e3
 $small_text_font_size: 22px
 $normal_text_font_size: 26px
 $highlight_text_font_size: 34px
 $mtop: 1.2%
 $mleft: 1.2%
 $image_margins_size: 1.2%
 $video_margins_size: 1.2%
 $canvas_margins_size: 1.2%
 $spline_scene_margins_size: 1.2%
--- a/styles/style.css
+++ b/styles/style.css
@ -0,0 +1,117 @@
 nav {
  width: 100%;
  height: 30px;
  -webkit-box-shadow: 0px 0px 20px #000;
          box-shadow: 0px 0px 20px #000;
  background-color: #895d5d;
 }
 canvas {
  margin-top: 2.4%;
  margin-bottom: 1.2%;
  -webkit-box-shadow: 10px 10px 24px #111;
          box-shadow: 10px 10px 24px #111;
 }
 .title {
  text-align: center;
  margin-top: 2%;
  margin-bottom: 2%;
  font-size: 60px;
  width: 100%;
  color: #d2d2d2;
 }
 .a {
  margin: 0% 5% 5% 5%;
  padding: 2%;
  border-radius: 10px;
  background-color: #313131;
  -webkit-box-shadow: 5px 5px 12px #141414;
          box-shadow: 5px 5px 12px #141414;
 }
 .normal_text {
  font-size: 26px;
  color: #d2d2d2;
  font-family: Arial, Helvetica, sans-ser;
  letter-spacing: 2px;
  background-color: #313131;
 }
 .highlight_text {
  font-size: 34px;
  color: #e3e3e3;
  font-family: Arial, Helvetica, sans-serif;
  letter-spacing: 1px;
  background-color: #313131;
 }
 .mtop {
  margin-top: 1.2%;
 }
 .mleft {
  margin-left: 1.2%;
 }
 .normal_image {
  margin-top: 2.4%;
  margin-bottom: 1.2%;
  -webkit-box-shadow: 10px 10px 24px #111;
          box-shadow: 10px 10px 24px #111;
 }
 .normal_video {
  margin-top: 2.4%;
  margin-bottom: 1.2%;
  -webkit-box-shadow: 10px 10px 24px #111;
          box-shadow: 10px 10px 24px #111;
 }
 .row {
  margin-top: 1.2%;
  display: -webkit-box;
  display: -ms-flexbox;
  display: flex;
  -ms-flex-pack: distribute;
      justify-content: space-around;
  -webkit-box-orient: horizontal;
  -webkit-box-direction: normal;
      -ms-flex-direction: row;
          flex-direction: row;
  border-radius: 10px;
 }
 .spline_scene {
  margin-top: 2.4%;
  margin-bottom: 1.2%;
  -webkit-box-shadow: 10px 10px 24px #111;
          box-shadow: 10px 10px 24px #111;
  width: 1000px;
  height: 600px;
 }
 * {
  padding: 0px;
  margin: 0px;
  -webkit-user-select: none;
     -moz-user-select: none;
      -ms-user-select: none;
          user-select: none;
  background-color: #282828;
  line-height: 1.3;
 }
 ::-webkit-scrollbar {
  width: 10px;
 }
 ::-webkit-scrollbar-track {
  background-color: #373737;
 }
 ::-webkit-scrollbar-thumb {
  background-color: #4b4b4b;
 }
 /*# sourceMappingURL=style.css.map */
--- a/styles/style.css.map
+++ b/styles/style.css.map
@ -0,0 +1,18 @@
 {
    "version": 3,
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    "sources": [
        "style.sass",
        "_main_tags.sass",
        "_variables.sass",
        "_classes.sass",
        "_variables.sass",
        "_mixins.sass",
        "_variables.sass",
        "_variables.sass",
        "_mixins.sass",
        "_variables.sass"
    ],
    "names": [],
    "file": "style.css"
 }
--- a/styles/style.sass
+++ b/styles/style.sass
@ -0,0 +1,20 @@
@import ./_main_tags
@import ./_classes
@import ./_variables
@import ./_mixins
 *
    padding: 0px
    margin: 0px
    user-select: none
    background-color: $primary
    line-height: 1.3
 ::-webkit-scrollbar
    width: 10px
 ::-webkit-scrollbar-track
    background-color: $scrollbar_track_color
 ::-webkit-scrollbar-thumb
    background-color: $scrollbar_thumb_color
--- a/videos/Terrain3D.mp4
+++ b/videos/Terrain3D.mp4
		`@ -0,0 +1,4 @@`

							`const app = new SpeRuntime.Application();`
							`app.start('./scene.json');`