Parametric curve
A parametric curve is a curve whose coordinates are expressed as functions of one or more parameters.
Geometry for Programmers
A parametric curve is a curve whose coordinates are specified as functions of one or more independent parameters.
- How it is used
- Deploys coordinate functions to represent programmable geometry for CAD, splines, games, and bitmap vectorization.
- How deep it goes
- Defines coordinate mappings and tangent vectors, then explains piecewise smoothness; defers tedious machine-formula representation to specialized software.
- Examples
- Uses joined linear and quadratic pieces, a boat-following spline, and bitmap vectorization as concrete applications.
- What you can do after
- Build piecewise curves by defining coordinate functions and controlling tangent directions at their joins.
Read how Geometry for Programmers explains parametric curve →
Deep Learning with R, Third Edition
A parametric curve is a curve whose points are determined by a finite set of parameters and one or more independent variables.
- How it is used
- Frames deep learning models as scalable fitted curves whose fixed parameters retrieve patterns during inference.
- How deep it goes
- Defines the analogy and explains training, inference, storage, retrieval, and distribution failure without formal curve mathematics.
- Examples
- Uses an ImageNet leopard-print sofa misclassification to illustrate failure outside the training distribution.
- What you can do after
- Evaluate why fixed fitted models retrieve familiar patterns yet struggle with novel situations.
Read how Deep Learning with R, Third Edition explains parametric curve →
Related concepts
- Bézier curveincludes · A Bézier curve is a parametric curve whose shape is determined by control points through Bernstein basis functions.
- rayused by · A ray is a geometric object with one endpoint that extends infinitely in a single direction.
- polynomial parametric curveincludes · A polynomial parametric curve is a curve whose coordinate functions are polynomials in its parameter.
- lineused by · A line is a contiguous sequence of text characters ending at a line boundary or the end of a text stream.
- tangent vectoruses · A tangent vector is a vector of first-order derivative values representing sensitivity or instantaneous direction under an input perturbation.
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