# Engineering Mathematics in Computer Graphics & Vision
> Explore how linear algebra, calculus, and probability power computer graphics, 3D rendering, and computer vision technologies.

Tags: computer-graphics, linear-algebra, computer-vision, engineering-math, rendering, image-processing, 3d-transformation
## Engineering Mathematics in Computer Graphics & Vision
* Transforming mathematical theory into visual reality.

## Linear Algebra & Transformations
* Matrices represent 3D transformations: rotation, scaling, and translation.
* Homogeneous coordinates enable affine transformations.
* Dot and cross products are essential for lighting calculations.
* Eigenvalues are used in PCA for dimensionality reduction.

## Coordinate Geometry & Projections
* 2D/3D coordinate systems define object positions.
* Perspective projection maps 3D scenes to 2D screens.
* Camera models utilize pinhole geometry (focal length, FOV).
* Ray-plane intersection techniques are used in ray tracing.

## Calculus in Rendering & Shading
* Derivatives compute surface normals for accurate light interaction.
* Integrals model global illumination through path tracing.
* Gradient descent optimizes neural rendering models.
* Bézier curves and NURBS use calculus for smooth interpolation.

## Probability, Statistics & Fourier Transforms
* Bayesian inference is used in object detection.
* Gaussian distributions model image noise.
* Fourier Transforms decompose images into frequency components for JPEG compression.
* Convolution theorem speeds up filtering via FFT.

## Real-World Applications
* **Game Development:** Real-time 3D transformations and physics engines.
* **Visual Effects (VFX):** Fluid simulation and motion blur.
* **Medical Imaging:** MRI reconstruction and CT scan processing.
* **AR/VR:** Spatial mapping and pose estimation.
* **Deep Learning:** Backpropagation and convolution.
---
This presentation was created with [Bobr AI](https://bobr.ai) — an AI presentation generator.