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Triangulation Visualizer

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About This MicroSim

This MicroSim demonstrates triangulation - the process of recovering 3D points from stereo correspondences. See how observation noise affects 3D reconstruction accuracy.

How to Use

  1. Adjust Baseline: Change the stereo camera separation
  2. Add Noise: Introduce measurement noise to observe error effects
  3. Drag Left Point: Manually adjust the left image observation
  4. Compare: See true point (green) vs triangulated point (red)
  5. Drag to Rotate: Change the 3D view angle

Key Concepts

Triangulation finds the 3D point P where rays from two cameras intersect.

Given: - Camera matrices P_L, P_R - Corresponding image points p_L, p_R

Solve: Find P such that p_L ~ P_L · P and p_R ~ P_R · P

Method Accuracy Speed
Mid-point Moderate Fast
Linear (DLT) Good Fast
Optimal Best Iterative

Learning Objectives

Students will be able to: - Understand how triangulation recovers 3D structure - Observe the effect of noise on reconstruction accuracy - Relate baseline to depth precision - Apply linear algebra to solve the triangulation problem

Lesson Plan

Introduction (5 minutes)

Triangulation is the core algorithm for 3D reconstruction from stereo. Given known camera geometry and corresponding points, we can recover depth.

Exploration (10 minutes)

  1. Start with zero noise - observe perfect reconstruction
  2. Add noise - see how the triangulated point deviates
  3. Increase baseline - observe improved depth precision
  4. Manually drag the left point to simulate matching errors

Key Insight

Longer baseline improves depth precision (reduces the uncertainty cone) but makes finding correspondences harder.

References