Geometry Engine

Euclidean, 4D Hypercube, and Exotic Topology.

Parameters

Shape

The Tesseract (4D Cube) rotates across multiple 4D hyper-planes.

Vertices: 16

Edges: 32

Faces: 24 (Squares)

Cells: 8 (Cubes)

Topology

Details

2D Computational Geometry Handbook

Mathematical Principles & Theorems

Investigates planar Euclidean and analytic geometry. Polygon area computed via Gauss's Shoelace formula: \(A = \frac{1}{2}|\sum_{i=1}^n (x_i y_{i+1} - x_{i+1} y_i)|\). Line-line intersection via determinant Cramer's rule. Circle circumcenter and incenter constructions. 2D affine transformation matrices: \(\begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} a & b & t_x \\ c & d & t_y \\ 0 & 0 & 1 \end{bmatrix}\begin{bmatrix} x \\ y \\ 1 \end{bmatrix}\) covering rotation, scaling, reflection, and translation.

Operating Instructions

Select a shape: Polygon, Triangle, Circle, or Custom Vertex Path.
Click or drag on the canvas to place and modify geometric vertices.
Inspect real-time geometric readouts: Perimeter, Shoelace Area, Centroid coordinates, and Interior Angles.
Apply affine transformations (Rotate, Scale, Translate) to observe coordinate matrix operations.