A curve is a continuous one-dimensional path in space. In programming, curves turn geometric ideas into data that CAD systems, game engines, image-processing libraries, 3D printers, and GIS tools can manipulate. section 1.1 section 1.0
Analytic geometry gives a curve coordinates and a formula, making it suitable for computation. Continuity and smoothness let you assemble curves from pieces while controlling the properties the result should have. section 1.2 section 5.3.4
Common curve-building choices include:
- Line segments and arcs provide basic pieces for constructing a curve. section 5.3.4
- Polynomials provide flexible formulas for shaping curves computationally. section 1.2
- Splines and NURBS support general-purpose modeling tuned to engineering needs. section 1.2
From smooth geometry to a printer path
A 3D-printing workflow can convert smooth CAD surfaces into triangles, analyze whether the mesh is printable, and produce stacked contours for the printer. Curves therefore connect smooth geometric models with discrete manufacturing instructions. section 1.0
