Rotation 3x3 Matrix Visualizer

RotMatrix.jsx

import React, { useEffect, useRef, useState } from 'react';
import * as THREE from 'three';

const ThreeDCoordinateSystem = () => {
  const mountRef = useRef(null);
  const [rotationMatrix, setRotationMatrix] = useState([
    [1, 0, 0],
    [0, 1, 0],
    [0, 0, 1]
  ]);
  const [angleY, setAngleY] = useState(0);

  useEffect(() => {
    // Scene setup
    const scene = new THREE.Scene();
    scene.background = new THREE.Color(0xffffff);

    // Camera setup
    const camera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, 0.1, 1000);
    camera.position.set(2, 2, 5);
    camera.lookAt(0, 0, 0);

    // Renderer setup
    const renderer = new THREE.WebGLRenderer({ antialias: true });
    renderer.setSize(window.innerWidth, window.innerHeight);
    mountRef.current.appendChild(renderer.domElement);

    // Create origin point
    const originGeometry = new THREE.SphereGeometry(0.1, 32, 32);
    const originMaterial = new THREE.MeshBasicMaterial({ color: 0x000000 });
    const origin = new THREE.Mesh(originGeometry, originMaterial);
    scene.add(origin);

    // Create coordinate axes
    const axisLength = 3;
    
    // X-axis (red)
    const xAxisGeometry = new THREE.BufferGeometry();
    const xAxisPoints = [new THREE.Vector3(0, 0, 0), new THREE.Vector3(axisLength, 0, 0)];
    xAxisGeometry.setFromPoints(xAxisPoints);
    const xAxisMaterial = new THREE.LineBasicMaterial({ color: 0xff0000 });
    const xAxis = new THREE.Line(xAxisGeometry, xAxisMaterial);
    scene.add(xAxis);
    
    // X-axis arrow
    const xArrowGeometry = new THREE.ConeGeometry(0.1, 0.3, 32);
    const xArrowMaterial = new THREE.MeshBasicMaterial({ color: 0xff0000 });
    const xArrow = new THREE.Mesh(xArrowGeometry, xArrowMaterial);
    xArrow.position.set(axisLength, 0, 0);
    xArrow.rotation.z = -Math.PI / 2;
    scene.add(xArrow);

    // Y-axis (green)
    const yAxisGeometry = new THREE.BufferGeometry();
    const yAxisPoints = [new THREE.Vector3(0, 0, 0), new THREE.Vector3(0, axisLength, 0)];
    yAxisGeometry.setFromPoints(yAxisPoints);
    const yAxisMaterial = new THREE.LineBasicMaterial({ color: 0x00ff00 });
    const yAxis = new THREE.Line(yAxisGeometry, yAxisMaterial);
    scene.add(yAxis);
    
    // Y-axis arrow
    const yArrowGeometry = new THREE.ConeGeometry(0.1, 0.3, 32);
    const yArrowMaterial = new THREE.MeshBasicMaterial({ color: 0x00ff00 });
    const yArrow = new THREE.Mesh(yArrowGeometry, yArrowMaterial);
    yArrow.position.set(0, axisLength, 0);
    scene.add(yArrow);

    // Z-axis (blue)
    const zAxisGeometry = new THREE.BufferGeometry();
    const zAxisPoints = [new THREE.Vector3(0, 0, 0), new THREE.Vector3(0, 0, axisLength)];
    zAxisGeometry.setFromPoints(zAxisPoints);
    const zAxisMaterial = new THREE.LineBasicMaterial({ color: 0x0000ff });
    const zAxis = new THREE.Line(zAxisGeometry, zAxisMaterial);
    scene.add(zAxis);
    
    // Z-axis arrow
    const zArrowGeometry = new THREE.ConeGeometry(0.1, 0.3, 32);
    const zArrowMaterial = new THREE.MeshBasicMaterial({ color: 0x0000ff });
    const zArrow = new THREE.Mesh(zArrowGeometry, zArrowMaterial);
    zArrow.position.set(0, 0, axisLength);
    zArrow.rotation.x = Math.PI / 2;
    scene.add(zArrow);

    // Add grids to the XZ and XY planes - with light color and not part of the rotating scene
    const gridSize = 6;
    const gridDivisions = 6;
    
    // XZ plane grid (horizontal)
    const xzGridHelper = new THREE.GridHelper(gridSize, gridDivisions, 0xcccccc, 0xeeeeee);
    // Rotate grid to XZ plane (default is XY)
    xzGridHelper.rotation.x = Math.PI / 2;
    
    // XY plane grid (vertical)
    const xyGridHelper = new THREE.GridHelper(gridSize, gridDivisions, 0xcccccc, 0xeeeeee);
    // No rotation needed for XY plane as it's the default
    
    // Create a separate scene for the non-rotating elements
    const staticScene = new THREE.Scene();
    staticScene.add(xzGridHelper);
    staticScene.add(xyGridHelper);
    
    // Create a blurred circular path in the XZ plane - radius matches axis length
    const circleRadius = axisLength; // Set radius to match axis length
    const circleSegments = 128;
    const circleGeometry = new THREE.BufferGeometry();
    const circlePoints = [];
    
    for (let i = 0; i <= circleSegments; i++) {
      const theta = (i / circleSegments) * Math.PI * 2;
      circlePoints.push(new THREE.Vector3(
        circleRadius * Math.cos(theta),
        0,
        circleRadius * Math.sin(theta)
      ));
    }
    
    circleGeometry.setFromPoints(circlePoints);
    
    // Create material with glow effect
    const circleMaterial = new THREE.LineBasicMaterial({
      color: 0xff6600,
      transparent: true,
      opacity: 0.5,
      linewidth: 2
    });
    
    const circleLine = new THREE.Line(circleGeometry, circleMaterial);
    staticScene.add(circleLine);
    
    // Add multiple blurred circles for glow effect
    const blurLayers = 5;
    for (let i = 0; i < blurLayers; i++) {
      const opacity = 0.3 - (i * 0.05);
      const blurMaterial = new THREE.LineBasicMaterial({
        color: 0xff6600,
        transparent: true,
        opacity: opacity,
        linewidth: 1
      });
      
      const blurCircle = new THREE.Line(circleGeometry, blurMaterial);
      blurCircle.scale.set(1 + (i * 0.03), 1, 1 + (i * 0.03));
      staticScene.add(blurCircle);
    }

    // Add axis labels
    const addLabel = (text, position, color) => {
      const canvas = document.createElement('canvas');
      canvas.width = 128;
      canvas.height = 64;
      
      const context = canvas.getContext('2d');
      context.fillStyle = '#ffffff';
      context.fillRect(0, 0, canvas.width, canvas.height);
      
      context.font = '48px Arial';
      context.fillStyle = color;
      context.textAlign = 'center';
      context.textBaseline = 'middle';
      context.fillText(text, canvas.width / 2, canvas.height / 2);
      
      const texture = new THREE.CanvasTexture(canvas);
      const material = new THREE.SpriteMaterial({ map: texture });
      const sprite = new THREE.Sprite(material);
      sprite.position.copy(position);
      sprite.scale.set(0.5, 0.25, 1);
      scene.add(sprite);
    };

    addLabel('X', new THREE.Vector3(axisLength + 0.3, 0, 0), '#ff0000');
    addLabel('Y', new THREE.Vector3(0, axisLength + 0.3, 0), '#00ff00');
    addLabel('Z', new THREE.Vector3(0, 0, axisLength + 0.3), '#0000ff');

    // Animation loop
    let rotate = true;
    let time = 0;
    
    const animate = () => {
      requestAnimationFrame(animate);
      
      if (rotate) {
        time += 0.01;
        
        // Only rotate around Y-axis as requested
        const newAngleY = time * 0.5;
        setAngleY(newAngleY);
        
        // Create rotation matrix for Y-axis only
        const cosY = Math.cos(newAngleY);
        const sinY = Math.sin(newAngleY);
        
        // Y-axis rotation matrix (keeps Y-axis as 0,1,0)
        // Transposed from typical presentation - rows are now X, Y, Z axes
        const rotY = [
          [cosY, 0, sinY],
          [0, 1, 0],
          [-sinY, 0, cosY]
        ];
        
        // Apply rotation to scene
        scene.rotation.x = 0;
        scene.rotation.y = newAngleY;
        scene.rotation.z = 0;
        
        // Set the rotation matrix (Y-axis rotation only)
        setRotationMatrix(rotY);
      }
      
      renderer.render(scene, camera);
      renderer.autoClear = false;
      renderer.render(staticScene, camera);
      renderer.autoClear = true;
    };
    
    animate();

    // Add controls for rotation
    const handleKeyDown = (e) => {
      if (e.key === ' ') {
        rotate = !rotate;
      }
    };

    window.addEventListener('keydown', handleKeyDown);

    // Handle window resize
    const handleResize = () => {
      camera.aspect = window.innerWidth / window.innerHeight;
      camera.updateProjectionMatrix();
      renderer.setSize(window.innerWidth, window.innerHeight);
    };

    window.addEventListener('resize', handleResize);

    // Cleanup
    return () => {
      window.removeEventListener('keydown', handleKeyDown);
      window.removeEventListener('resize', handleResize);
      mountRef.current.removeChild(renderer.domElement);
    };
  }, []);

  // Convert angle to degrees and π representation
  const angleYDegrees = (angleY * 180 / Math.PI) % 360;
  
  // Create pi representation (e.g., 0.5π, 1π, 1.5π)
  const getPiNotation = (radians) => {
    // Normalize to 0-2π range
    const normalized = radians % (2 * Math.PI);
    const inPiUnits = normalized / Math.PI;
    
    // Format based on value
    if (Math.abs(inPiUnits) < 0.01) return "0";
    if (Math.abs(inPiUnits - 1) < 0.01) return "π";
    if (Math.abs(inPiUnits - 2) < 0.01) return "2π";
    if (Math.abs(inPiUnits - 0.5) < 0.01) return "π/2";
    if (Math.abs(inPiUnits - 1.5) < 0.01) return "3π/2";
    
    // For other values, format as Nπ
    const formatted = Math.round(inPiUnits * 100) / 100;
    return `${formatted}π`;
  };
  
  // Format angle display
  const formatAngle = (angle) => {
    return Math.round(angle * 100) / 100;
  };
  
  // Get calculated values for display
  const cosY = Math.cos(angleY);
  const sinY = Math.sin(angleY);
  const roundedCosY = Math.round(cosY * 100) / 100;
  const roundedSinY = Math.round(sinY * 100) / 100;

  return (
    <div className="w-full h-screen">
      <div ref={mountRef} className="w-full h-full" />
      
      {/* Rotation Matrix Display */}
      <div className="absolute top-4 right-4 bg-white p-4 rounded shadow">
        <h3 className="font-bold mb-2 text-center">Y-Axis Rotation Matrix</h3>
        
        {/* Angle Display */}
        <div className="mb-3 text-center">
          <div>θ = {getPiNotation(angleY)} = {formatAngle(angleYDegrees)}°</div>
        </div>
        
        {/* Matrix with cosine/sine notation - Mathematical style */}
        <div className="border-2 border-gray-300 p-4 rounded mb-3 flex items-center justify-center">
          <div className="text-3xl mr-2">(</div>
          <div>
            <div className="flex justify-center">
              <div className="w-16 flex items-center justify-center m-1 text-red-600 font-mono">cos(θ)</div>
              <div className="w-16 flex items-center justify-center m-1 text-red-600 font-mono">0</div>
              <div className="w-16 flex items-center justify-center m-1 text-red-600 font-mono">sin(θ)</div>
            </div>
            <div className="flex justify-center">
              <div className="w-16 flex items-center justify-center m-1 text-green-600 font-mono">0</div>
              <div className="w-16 flex items-center justify-center m-1 text-green-600 font-mono">1</div>
              <div className="w-16 flex items-center justify-center m-1 text-green-600 font-mono">0</div>
            </div>
            <div className="flex justify-center">
              <div className="w-16 flex items-center justify-center m-1 text-blue-600 font-mono">-sin(θ)</div>
              <div className="w-16 flex items-center justify-center m-1 text-blue-600 font-mono">0</div>
              <div className="w-16 flex items-center justify-center m-1 text-blue-600 font-mono">cos(θ)</div>
            </div>
          </div>
          <div className="text-3xl ml-2">)</div>
        </div>
        
        {/* Matrix with calculated values - Mathematical style */}
        <h4 className="text-center mb-1">Current Values:</h4>
        <div className="border-2 border-gray-300 p-4 rounded flex items-center justify-center">
          <div className="text-3xl mr-2">(</div>
          <div>
            <div className="flex justify-center">
              <div className="w-16 flex items-center justify-center m-1 text-red-600 font-mono">{roundedCosY}</div>
              <div className="w-16 flex items-center justify-center m-1 text-red-600 font-mono">0</div>
              <div className="w-16 flex items-center justify-center m-1 text-red-600 font-mono">{roundedSinY}</div>
            </div>
            <div className="flex justify-center">
              <div className="w-16 flex items-center justify-center m-1 text-green-600 font-mono">0</div>
              <div className="w-16 flex items-center justify-center m-1 text-green-600 font-mono">1</div>
              <div className="w-16 flex items-center justify-center m-1 text-green-600 font-mono">0</div>
            </div>
            <div className="flex justify-center">
              <div className="w-16 flex items-center justify-center m-1 text-blue-600 font-mono">-{Math.abs(roundedSinY)}</div>
              <div className="w-16 flex items-center justify-center m-1 text-blue-600 font-mono">0</div>
              <div className="w-16 flex items-center justify-center m-1 text-blue-600 font-mono">{roundedCosY}</div>
            </div>
          </div>
          <div className="text-3xl ml-2">)</div>
        </div>
        
        <div className="mt-2 text-sm">
          <div className="flex items-center">
            <div className="w-4 h-4 bg-red-600 mr-2"></div>
            <span>X axis (row 1)</span>
          </div>
          <div className="flex items-center">
            <div className="w-4 h-4 bg-green-600 mr-2"></div>
            <span>Y axis (row 2)</span>
          </div>
          <div className="flex items-center">
            <div className="w-4 h-4 bg-blue-600 mr-2"></div>
            <span>Z axis (row 3)</span>
          </div>
        </div>
      </div>
      
      <div className="absolute bottom-4 left-4 bg-white p-2 rounded shadow">
        <p className="text-sm">Press spacebar to toggle rotation</p>
      </div>
    </div>
  );
};

export default ThreeDCoordinateSystem;

Demo:

https://claude.site/artifacts/39cead57-9d73-408a-ab7b-7e309d80af73