Engineering Mathematics in Computer Graphics & Vision

Explore how linear algebra, calculus, and probability power computer graphics, 3D rendering, and computer vision technologies.

#computer-graphics#linear-algebra#computer-vision#engineering-math#rendering#image-processing#3d-transformation

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Engineering Mathematics

Application of Engineering Mathematics

in Computer Graphics & Vision

Transforming mathematical theory into visual reality

Presented by: [Student Name] | Department of Computer Science

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OVERVIEW

Core Concepts & Applications

MODULE 01

Linear Algebra & Transformations

MODULE 02

Coordinate Geometry & Projections

MODULE 03

Calculus in Rendering & Shading

MODULE 04

Probability & Statistics in Computer Vision

MODULE 05

Fourier Transform & Image Processing

MODULE 06

Conclusion & Applications

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01 | Linear Algebra

Linear Algebra & Transformations

Matrices represent 3D transformations (rotation, scaling, translation)

Homogeneous coordinates enable affine transformations

Dot & cross products used for lighting calculations

Eigenvalues used in PCA for dimensionality reduction

Applied in: OpenGL, DirectX transformation pipelines

R(θ) =

Core Formula
2D Rotation Matrix

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02 | Coordinate Geometry

Coordinate Geometry & Projections

2D/3D coordinate systems define object positions in space

Perspective projection maps 3D scenes to 2D screens

Camera models use pinhole geometry (focal length, FOV)

Ray-plane intersection used in ray tracing

Homography transforms used in image stitching & AR

Perspective Projection Equation (z-division)

x' = f · (X / Z)
y' = f · (Y / Z)

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03 | CALCULUS

Calculus in Rendering & Shading

Derivatives compute surface normals for accurate lighting

Integrals model global illumination (path tracing)

Gradient descent optimizes neural rendering models

Partial derivatives used in texture mapping & bump mapping

Bézier curves & NURBS use calculus for smooth interpolation

L_o = L_e + ∫ _Ω f_r · L_i · (ω_i · n) dω_i

Core Formula
The Rendering Equation

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04 | Probability & Statistics

Probability & Statistics in Vision

Bayesian inference in object detection

Gaussian distributions model image noise

Histogram analysis for image segmentation

Statistical learning in feature matching (SIFT, ORB)

05 | Fourier Transform

Fourier Transform & Image Processing

Decompose images into frequency components

Low-pass filters blur; high-pass filters sharpen

Used in JPEG compression algorithms

Convolution theorem speeds up filtering (FFT)

Edge detection via frequency domain analysis

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06 | Conclusion

Conclusion & Real-World Applications

🎮 Game Development

Real-time 3D transformations, physics engines

🤖 Computer Vision

Object detection, face recognition, SLAM

🎬 Visual Effects (VFX)

Ray tracing, fluid simulation, motion blur

🏥 Medical Imaging

MRI reconstruction, CT scan processing

🥽 AR / VR

Spatial mapping, depth sensing, pose estimation

🧠 Deep Learning

Backpropagation, convolution, optimization

"Engineering Mathematics is the invisible engine powering every pixel you see."

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