Geomatic Examples

Explore interactive demonstrations of geometric concepts using the Geomatic system.

• Cardioid

  Visualize a cardioid (heart-shaped curve) as a family of circles. Demonstrates broadcasting to create points on a circle and draw circles to form the cardioid envelope.

• Peaucellier-Lipkin Linkage

  The first planar linkage to produce exact straight line motion from rotary motion. Watch how a rotating hand is translated into linear motion through circle intersections and reflection.

• Finding Square Root with Gradient Descent

  Learn how to find square roots using gradient descent optimization. Start with a random guess and converge towards the correct value by iteratively calculating loss, backpropagating, and taking gradient descent steps.

• Gradient of an Angle

  Connect geometry and calculus by demonstrating that the gradient of an angle of a triangle always points towards its circumcenter. Uses autograd to visualize the orthogonality property of the gradient.

• Fermat Point of a Triangle

  Find the Fermat point (the point that minimizes total distance to all triangle vertices) using gradient descent. Iteratively minimize the sum of distances by computing loss, backpropagating, and taking gradient descent steps.