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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,
+    "mappings": "ACEA,AAAA,GAAG,CAAC;EACA,KAAK,EAAE,IAAI;EACX,MAAM,EAAE,IAAI;EACZ,UAAU,EAAE,iBAAiB;EAC7B,gBAAgB,ECLL,OAAO;CDKgB;;AAEtC,AAAA,MAAM,CAAC;EACH,UAAU,EAAE,IAA4B;EACxC,aAAa,ECOK,IAAI;EDNtB,UAAU,EAAE,mBAAmB;CAAG;;AERtC,AAAA,MAAM,CAAC;EACH,UAAU,EAAE,MAAM;EAClB,UAAU,EAAE,EAAE;EACd,aAAa,EAAE,EAAE;EACjB,SAAS,EAAE,IAAI;EACf,KAAK,EAAE,IAAI;EACX,KAAK,EDFM,OAAO;CCEK;;AAE3B,AAAA,EAAE,CAAC;EACC,MAAM,EAAE,WAAW;EACnB,OAAO,EAAE,EAAE;EACX,aAAa,EAAE,IAAI;EACnB,gBAAgB,EDbJ,OAAO;ECcnB,UAAU,EAAG,GAAG,CAAC,GAAG,CAAC,IAAI,CAAC,OAAO;CAAK;;AAE1C,AAAA,YAAY,CAAC;EEPT,SAAS,EHDW,IAAI;EGExB,KAAK,EHLM,OAAO;EGMlB,WAAW,EAAE,0BAA0B;EACvC,cAAc,EAAE,GAAG;EFMnB,gBAAgB,EDlBJ,OAAO;CCkBgB;;AAEvC,AAAA,eAAe,CAAC;EELZ,SAAS,EHNc,IAAI;EGO3B,KAAK,EHVM,OAAO;EGWlB,WAAW,EAAE,4BAA4B;EACzC,cAAc,EAAE,GAAG;EFInB,gBAAgB,EDtBJ,OAAO;CCsBgB;;AAEvC,AAAA,KAAK,CAAC;EACF,UAAU,EDfP,IAAI;CCea;;AAExB,AAAA,MAAM,CAAC;EACH,WAAW,EDjBP,IAAI;CCiBc;;AAE1B,AAAA,aAAa,CAAC;EACV,UAAU,EAAE,IAA2B;EACvC,aAAa,EDnBI,IAAI;ECoBrB,UAAU,EAAE,mBAAmB;CAAG;;AAEtC,AAAA,aAAa,CAAC;EACV,UAAU,EAAE,IAA2B;EACvC,aAAa,EDvBI,IAAI;ECwBrB,UAAU,EAAE,mBAAmB;CAAG;;AAEtC,AAAA,IAAI,CAAC;EACD,UAAU,ED/BP,IAAI;ECgCP,OAAO,EAAE,IAAI;EACb,eAAe,EAAE,YAAY;EAC7B,cAAc,EAAE,GAAG;EACnB,aAAa,EAAE,IAAI;CAAG;;AAE1B,AAAA,aAAa,CAAC;EACV,UAAU,EAAE,IAAkC;EAC9C,aAAa,EDjCW,IAAI;ECkC5B,UAAU,EAAE,mBAAmB;EAC/B,KAAK,EAAE,MAAM;EACb,MAAM,EAAE,KAAK;CAAG;;AHjDpB,AAAA,CAAC,CAAC;EACE,OAAO,EAAE,GAAG;EACZ,MAAM,EAAE,GAAG;EACX,WAAW,EAAE,IAAI;EACjB,gBAAgB,EETV,OAAO;EFUb,WAAW,EAAE,GAAG;CAAG;;AAEvB,AAAA,mBAAmB,CAAC;EAChB,KAAK,EAAE,IAAI;CAAG;;AAElB,AAAA,yBAAyB,CAAC;EACtB,gBAAgB,EEZI,OAAO;CFYgB;;AAE/C,AAAA,yBAAyB,CAAC;EACtB,gBAAgB,EEdI,OAAO;CFcgB",
+    "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