Geometry Playground

Project Goal

외부 라이브러리에 의존하지 않고
컴퓨터 비전(Computer Vision), 3D Geometry, Camera Calibration, 3D Reconstruction, Photometric Stereo 등을
직접 구현하는 것을 목표로 하는 프로젝트.

최종 목표!!

• Math &Geometry Library (Vector, Matrix, Quaternion, Rotation, Transform, Plane, Ray ...)
• Calibration Toolkit
• OpticalFlow Library
• 3D Reconstruction Pipeline

ComputerVisionPortfolio/
├─ GeometryPlayground/    <-해당
│  └─ Geometry.Core/
│  └─ ...
│
├─ CameraCalibrationToolkit/
│  ├─ CameraCalibrationToolkit.sln
│  └─ Calibration.Core/
│  └─ ...
│
└─ OpticalFlowLibrary/
│  ├─ OpticalFlowLibrary.sln
│  └─ OpticalFlow.Core/
│  └─ ...
│
└─ 3DReconstructionPipeline/
   ├─ 3DReconstruction.sln
   └─ 3DReconstruction.Core/
   └─ ...

---

Current Progress

Project Structure

GeometryPlayground
│
├── Geometry.Core
│   ├── Math
│   │   ├── DoubleVector
│   │   ├── DoubleMatrix
│   │   └── Utils
│   │
│   └── Geometry
│       ├── Rotation
│       └── Transform
│
└── Geometry.Demo



GeometryPlayground
├─ Math
│  ├─ Vector              <- 작업 완료
│  ├─ Matrix              <- 작업 완료
│  ├─ SVD                 <- 작업 예정
│  ├─ LeastSquares        <- 작업 예정
│  └─ Utils               <- 작업 중
│
├─ Geometry
│  ├─ Rotation            <- 작업 중
│  ├─ Quaternion          <- 작업 중
│  ├─ Transform           <- 작업 중
│  ├─ Plane               <- 작업 예정
│  ├─ Ray                 <- 작업 예정
│  └─ Line                <- 작업 예정
│
├─ ProjectiveGeometry
│  ├─ HomogeneousCoordinate
│  ├─ Projection
│  ├─ Homography
│  └─ Triangulation
│
├─ Optimization
│  ├─ GaussNewton
│  ├─ LevenbergMarquardt
│  └─ RANSAC
│
└─ Demo

Implemented

Math

• Vec2d
• Vec3d
• Mat2d
• Mat3d
• Mat4d

Implemented Features

• Matrix / Vector Arithmetic
• Matrix Multiplication
• Transpose
• Determinant
• Cofactor Matrix
• Adjugate Matrix
• Inverse
• Identity
• IsApprox

Geometry

Rotation

Implemented

• Rodrigues Formula
• Skew Symmetric Matrix
• Rotation Matrix Validation

Verified using

RᵀR = I
det(R) = 1

Transform

Implemented

• Identity
• Translate
• Rotate
• FromRotationTranslation
• Inverse

Transformation Matrix

[ R11 R12 R13 tx ]
[ R21 R22 R23 ty ]
[ R31 R32 R33 tz ]
[  0   0   0  1 ]

Inverse Transformation

[ Rᵀ  -Rᵀt ]
[  0     1 ]

Demo

Implemented demo programs for

• Rodrigues Rotation
• Rotation Matrix Verification
• Transformation Matrix
• Inverse Transformation

Verified using

T × T⁻¹ = I

---

Next Step

Camera
    ↓
Calibration Toolkit
    ↓
3D Reconstruction Pipeline
    ↓
Photometric Stereo