Cornu Spiral Evolution

Watch the evolution of a Cornu spiral with its osculating circle - the tangential circle that matches the spiral's curvature at its tip

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Cornu Spiral
Osculating Circle
Spiral Tip
Circle Center
About the Cornu Spiral:
The Cornu spiral (also called the Euler spiral or clothoid) is a curve whose curvature increases linearly with arc length. The osculating circle at any point is the unique circle that best approximates the curve at that point, sharing the same tangent direction and curvature. As you move along the spiral, watch how the radius of the osculating circle decreases (curvature increases) and how its center moves to maintain tangency with the spiral tip.