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Create new applet for alternative basis
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73 changes: 73 additions & 0 deletions
73
src/routes/applet/change_of_basis/alternative_basis/+page.svelte
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,73 @@ | ||
| <script> | ||
| import Canvas2D from '$lib/d3/Canvas2D.svelte'; | ||
| import { Vector2 } from 'three'; | ||
| import TransformedAxis from './TransformedAxis.svelte'; | ||
| import Vector2D from '$lib/d3/Vector2D.svelte'; | ||
| import { PrimeColor } from '$lib/utils/PrimeColors'; | ||
| import Latex2D from '$lib/d3/Latex2D.svelte'; | ||
| import { Draggable } from '$lib/controls/Draggables.svelte'; | ||
| import { round } from '$lib/utils/MathLib'; | ||
| import { Formula } from '$lib/utils/Formulas'; | ||
| const b1 = new Vector2(1, 3); | ||
| const b2 = new Vector2(2, 1); | ||
| const draggables = [new Draggable(new Vector2(6, -2))]; | ||
| const x = $derived(draggables[0].value.x); | ||
| const y = $derived(draggables[0].value.y); | ||
| const c1 = $derived(x + (2 / 5) * (y - 3 * x)); | ||
| const c2 = $derived((-1 / 5) * (y - 3 * x)); | ||
| const formulas = $derived.by(() => { | ||
| const vec = `\\begin{bmatrix} ${round(x)} \\\\ ${round(y)} \\end{bmatrix}`; | ||
| const f1 = new Formula('\\$1 = \\$2 \\$3 + \\$4 \\$5') | ||
| .addAutoParam(vec, PrimeColor.blue) | ||
| .addAutoParam(round(c1), PrimeColor.cyan) | ||
| .addAutoParam('\\mathbf{b_1}', PrimeColor.raspberry) | ||
| .addAutoParam(round(c2), PrimeColor.cyan) | ||
| .addAutoParam('\\mathbf{b_2}', PrimeColor.raspberry); | ||
| return [f1]; | ||
| }); | ||
| </script> | ||
|
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| <Canvas2D customAxis {draggables} {formulas} showFormulasDefault cameraZoom={0.5}> | ||
| <TransformedAxis basis={[b1, b2]} /> | ||
|
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| <!-- Basis --> | ||
| <Vector2D direction={b1} length={b1.length()} color={PrimeColor.raspberry} /> | ||
| <Latex2D latex={'\\mathbf{b_1}'} position={b1} extend={0.2} color={PrimeColor.raspberry} /> | ||
|
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| <Vector2D direction={b2} length={b2.length()} color={PrimeColor.raspberry} /> | ||
| <Latex2D latex={'\\mathbf{b_2}'} position={b2} extend={0.2} color={PrimeColor.raspberry} /> | ||
|
|
||
| <!-- Compound --> | ||
| <Vector2D | ||
| direction={b1.clone().multiplyScalar(c1)} | ||
| length={b1.clone().multiplyScalar(c1).length()} | ||
| color={PrimeColor.cyan} | ||
| /> | ||
| <Latex2D | ||
| latex={`\\mathbf{${round(c1)} b_1}`} | ||
| position={b1.clone().multiplyScalar(c1)} | ||
| extend={0.2} | ||
| color={PrimeColor.cyan} | ||
| /> | ||
|
|
||
| <Vector2D | ||
| origin={b1.clone().multiplyScalar(c1)} | ||
| direction={b2.clone().multiplyScalar(c2)} | ||
| length={b2.clone().multiplyScalar(c2).length()} | ||
| color={PrimeColor.cyan} | ||
| /> | ||
| <Latex2D | ||
| latex={`\\mathbf{${round(c2)}b_2}`} | ||
| offset={b1.clone().multiplyScalar(c1)} | ||
| position={b2.clone().multiplyScalar(c2)} | ||
| extend={0.2} | ||
| color={PrimeColor.cyan} | ||
| /> | ||
| </Canvas2D> |
102 changes: 102 additions & 0 deletions
102
src/routes/applet/change_of_basis/alternative_basis/TransformedAxis.svelte
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,102 @@ | ||
| <script lang="ts"> | ||
| import Latex2D from '$lib/d3/Latex2D.svelte'; | ||
| import { GRID_SIZE_2D } from '$lib/utils/AttributeDimensions'; | ||
| import { PrimeColor } from '$lib/utils/PrimeColors'; | ||
| import { Vector2 } from 'three'; | ||
| type AxisProps = { | ||
| length?: number; | ||
| showOrigin?: boolean; | ||
| basis: [Vector2, Vector2]; | ||
| showAxisNumbers?: boolean; | ||
| }; | ||
| let { | ||
| length = GRID_SIZE_2D, | ||
| showOrigin = true, | ||
| showAxisNumbers = true, | ||
| basis = [new Vector2(1, 0), new Vector2(0, 1)] | ||
| }: AxisProps = $props(); | ||
| // Generate indeces for the grid lines from -length to length including 0 | ||
| let axisIndeces = $derived([...Array(length + 1).keys()].flatMap((a) => [-a, a])); | ||
| function stokeWidth(index: number) { | ||
| if (index % 10 == 0) return 0.02; | ||
| if (index % 5 == 0) return 0.01; | ||
| return 0.005; | ||
| } | ||
| function radiansToDegrees(radians: number) { | ||
| return radians * (180 / Math.PI); | ||
| } | ||
| let xRotation = radiansToDegrees(Math.atan(basis[0].y / basis[0].x)); | ||
| let yRotation = radiansToDegrees(Math.atan(-basis[1].x / basis[1].y)); | ||
| </script> | ||
|
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||
| <g> | ||
| <line | ||
| x1={0} | ||
| y1={-length} | ||
| x2={0} | ||
| y2={length} | ||
| stroke={PrimeColor.black + PrimeColor.opacity(0.5)} | ||
| stroke-width={0.04} | ||
| /> | ||
| <line | ||
| x1={-length} | ||
| y1={0} | ||
| x2={length} | ||
| y2={0} | ||
| stroke={PrimeColor.black + PrimeColor.opacity(0.5)} | ||
| stroke-width={0.04} | ||
| /> | ||
|
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| {#each axisIndeces as index} | ||
| <!-- Grid Lines --> | ||
| <line | ||
| transform="rotate({yRotation}) scale({basis[1].length()})" | ||
| x1={index} | ||
| y1={-length} | ||
| x2={index} | ||
| y2={length} | ||
| stroke={PrimeColor.black + PrimeColor.opacity(0.5)} | ||
| stroke-width={stokeWidth(index)} | ||
| /> | ||
| <line | ||
| transform="rotate({xRotation}) scale({basis[0].length() / 2})" | ||
| x1={-length} | ||
| y1={index} | ||
| x2={length} | ||
| y2={index} | ||
| stroke={PrimeColor.black + PrimeColor.opacity(0.5)} | ||
| stroke-width={stokeWidth(index)} | ||
| /> | ||
|
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| <!-- Tick marks --> | ||
| <line x1={index} y1={-0.1} x2={index} y2={0.1} stroke="black" stroke-width={0.02} /> | ||
| <line x1={-0.1} y1={index} x2={0.1} y2={index} stroke="black" stroke-width={0.02} /> | ||
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| {#if index != 0 && showAxisNumbers} | ||
| <!-- X axis number labels --> | ||
| {#if index > 0 && index % 2 == 0} | ||
| <Latex2D latex={index.toLocaleString()} position={new Vector2(index - 0.07, -0.15)} /> | ||
| {:else if index % 2 == 0} | ||
| <Latex2D latex={index.toLocaleString()} position={new Vector2(index - 0.15, -0.15)} /> | ||
| {/if} | ||
|
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| <!-- Y axis number labels --> | ||
| {#if index > 0 && index % 2 == 0} | ||
| <Latex2D latex={index.toLocaleString()} position={new Vector2(-0.3, index + 0.12)} /> | ||
| {:else if index % 2 == 0} | ||
| <Latex2D latex={index.toLocaleString()} position={new Vector2(-0.55, index + 0.1)} /> | ||
| {/if} | ||
| {/if} | ||
| {/each} | ||
|
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| <!-- Axis labels --> | ||
| {#if showOrigin} | ||
| <Latex2D latex={'O'} offset={new Vector2(-0.28, -0.11)} /> | ||
| {/if} | ||
| </g> |