Tangent
A tangent line is a line that touches a curve at a point and represents its instantaneous direction there.
Geometry for Programmers
A tangent line is the line that touches a curve at a point and represents the curve's instantaneous direction there.
- How it is used
- Explains instantaneous curve direction and constrains polynomial joins to preserve smoothness.
- How deep it goes
- Builds geometric intuition from shrinking intervals, then applies derivative equations to interpolation and curvature constraints.
- Examples
- Uses shrinking secant intervals, a cubic through two points, and matching tangent slopes of -1.
- What you can do after
- Apply tangent slopes to measure local direction and construct smooth polynomial curves with derivative constraints.
Advanced Algorithms and Data Structures
A tangent is a line that touches a curve at a point and represents its instantaneous direction there.
- How it is used
- Uses curve direction to guide Bézier intersection detection and subdivision.
- How deep it goes
- Explains tangent placement and its algorithmic use, but defers generic Bézier clipping details.
- Examples
- Uses symmetric quadratic Bézier curves, axis-parallel tangents, subdivision diagrams, and segment approximations.
- What you can do after
- Apply tangents to split Bézier curves into monotonic sections for approximate intersection testing.
Read how Advanced Algorithms and Data Structures explains tangent →
Related concepts
- derivativemeasured by · A derivative is a mathematical quantity that measures the instantaneous rate of change of a function with respect to an input variable.
- elliptic curve point additionused by · Elliptic-curve point addition combines two curve points according to the curve's group law to produce another curve point.
- Miller's algorithmused by · An iterative algorithm for computing an elliptic-curve pairing by evaluating the required rational functions through doubling and addition steps.
- linear approximationequivalent to · Linear approximation represents a differentiable function near a point with a linear function determined by its value and first derivative there.
- tangent vectorcontrasts with · A tangent vector is a vector of first-order derivative values representing sensitivity or instantaneous direction under an input perturbation.
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