Interactive Calculus Visualizer

{"name":"Riemann Sum","description":"","photo":"https://res.cloudinary.com/dzv7hjwfn/image/upload/Assets/PixelNook/elder","view_count":3,"fork_count":0,"expires_at":null,"created_at":"2025-09-14T13:10:21.878731Z","updated_at":"2025-09-14T13:10:21.878732Z","user_id":null,"status":"PUBLIC","parent_id":null,"id":9863,"user":null,"code":{"script.js":"function setup() {\n createCanvas(windowWidth, windowHeight);\n background(135, 206, 235); // Sky blue background\n}\n\nfunction draw() {\n background(135, 206, 235); // Clear the background each frame\n drawRiemannSums();\n}\n\nfunction drawRiemannSums() {\n let a = 0; // Start of the interval\n let b = TWO_PI; // End of the interval\n let n = 100; // Number of rectangles\n\n let dx = (b - a) / n; // Width of each rectangle\n let scaleX = width / (b - a); // Scale for x-axis\n let scaleY = height / 2; // Scale for y-axis\n\n translate(0, height / 2); // Center the y-axis\n\n stroke(0);\n strokeWeight(1);\n noFill();\n\n // Draw the function curve\n beginShape();\n for (let x = a; x <= b; x += 0.01) {\n let y = sin(x);\n vertex(x * scaleX, -y * scaleY); // Invert y for drawing\n }\n endShape();\n\n // Draw the Riemann rectangles\n fill(255, 100, 100, 150); // Semi-transparent red\n for (let i = 0; i < n; i++) {\n let x = a + i * dx;\n let y = sin(x);\n rect(x * scaleX, 0, dx * scaleX, -y * scaleY); // Invert y for rectangle height\n }\n}\n\n","style.css":"body { margin: 0; } canvas { display: block; }","index.html":"\n\n\n \n \n Interactive Calculus Visualizer\n \n \n \n \n\n\n \n\n"},"chat_history":[{"message":"calculus visualiser","project_id":9863,"created_at":"2025-09-14T13:08:10.416249Z","output_tokens":null,"sender":"human","code_id":281727,"deleted":0,"input_tokens":null,"id":170850},{"message":"Let's get started!\n Errors:\n","project_id":9863,"created_at":"2025-09-14T13:08:15.795989Z","output_tokens":null,"sender":"client_script","code_id":281727,"deleted":0,"input_tokens":null,"id":170851},{"message":"Great! It sounds like you're working on an interactive calculus visualizer. Could you tell me a bit more about what you'd like your visualizer to do? For example, are you interested in visualizing specific calculus concepts like derivatives, integrals, or something else?","project_id":9863,"created_at":"2025-09-14T13:08:16.000755Z","output_tokens":67,"sender":"ai","code_id":281727,"deleted":0,"input_tokens":2616,"id":170852},{"message":"riemann sums","project_id":9863,"created_at":"2025-09-14T13:08:30.791503Z","output_tokens":null,"sender":"human","code_id":281727,"deleted":0,"input_tokens":null,"id":170853},{"message":"Visualizing Riemann sums is a fantastic way to understand the concept of integrals. We can create a series of rectangles under a curve to approximate the area under that curve. \n\nWould you like to visualize a specific function, or should we start with a simple one like \\( f(x) = x^2 \\)? Also, do you have any preferences for the number of rectangles or the range of the x-axis you want to visualize?","project_id":9863,"created_at":"2025-09-14T13:08:30.867929Z","output_tokens":100,"sender":"ai","code_id":281727,"deleted":0,"input_tokens":2614,"id":170854},{"message":"sin(x) then I can plug in whatever","project_id":9863,"created_at":"2025-09-14T13:08:47.786817Z","output_tokens":null,"sender":"human","code_id":281727,"deleted":0,"input_tokens":null,"id":170855},{"message":"Visualizing Riemann sums for the function \\( \\sin(x) \\) is a great start! We'll create rectangles to approximate the area under the curve of \\( \\sin(x) \\) over a specified interval. You can adjust the function later to try different ones.\n\nLet's start by setting up the basic visualization in the `draw()` function. I'll also include a simple way for you to change the number of rectangles.\n\n```javascript\n// script.js\nfunction setup() {\n createCanvas(windowWidth, windowHeight);\n background(135, 206, 235); // Sky blue background\n}\n\nfunction draw() {\n background(135, 206, 235); // Clear the background each frame\n drawRiemannSums();\n}\n\nfunction drawRiemannSums() {\n let a = 0; // Start of the interval\n let b = TWO_PI; // End of the interval\n let n = 10; // Number of rectangles\n\n let dx = (b - a) / n; // Width of each rectangle\n let scaleX = width / (b - a); // Scale for x-axis\n let scaleY = height / 2; // Scale for y-axis\n\n translate(0, height / 2); // Center the y-axis\n\n stroke(0);\n strokeWeight(1);\n noFill();\n\n // Draw the function curve\n beginShape();\n for (let x = a; x <= b; x += 0.01) {\n let y = sin(x);\n vertex(x * scaleX, -y * scaleY); // Invert y for drawing\n }\n endShape();\n\n // Draw the Riemann rectangles\n fill(255, 100, 100, 150); // Semi-transparent red\n for (let i = 0; i < n; i++) {\n let x = a + i * dx;\n let y = sin(x);\n rect(x * scaleX, 0, dx * scaleX, -y * scaleY); // Invert y for rectangle height\n }\n}\n```\n\n### Explanation:\n- **drawRiemannSums()**: This function draws the Riemann sum visualization.\n- **a and b**: Define the interval [0, 2π] for the function.\n- **n**: Number of rectangles used to approximate the area.\n- **Scale**: `scaleX` and `scaleY` scale the function to fit the canvas.\n- **translate()**: Centers the y-axis to make the visualization clearer.\n- **beginShape() / endShape()**: Draws the sin(x) curve.\n- **rect()**: Draws the rectangles for the Riemann sum.\n\nYou can change the number of rectangles by adjusting the value of `n`. Let me know if you'd like to add or change anything!","project_id":9863,"created_at":"2025-09-14T13:08:47.987769Z","output_tokens":534,"sender":"ai","code_id":281727,"deleted":0,"input_tokens":2620,"id":170856},{"message":"

Load your new image into your code:

\n\n```javascript\nfunction preload() {\n\n\telder = loadImage(\"@asset('elder')\");\n}\n```","project_id":9863,"created_at":"2025-09-14T13:10:04.472534Z","output_tokens":null,"sender":"server_script","code_id":281730,"deleted":0,"input_tokens":null,"id":170857}],"assets":[{"project_id":9863,"creator":"","cloudinary_id":"Assets/PixelNook/elder","deleted":false,"id":85624,"created_at":"2025-09-14T13:10:04.064321Z","name":"elder","resource_type":"image","tags":["Character","Pixel art"]}],"messages_sent":3,"comments":[],"steps":[]}