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A modern flexible curve. A related but distinct device is the "flexible curve", which can be molded by hand and used to design or copy a complex curve. Unlike a spline, the flexible curve does not have significant tension, so it maintains a given shape, instead of minimizing its curvature between point.
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
A French curve is a drawing aid with many different smoothly-varying radiused curves on it; the manual drafter can fit the French curve to some known reference points and draw a smooth curved line between them. A spline is a flexible ruler, usually rubber or plastic coated with a metal "backbone", which can be smoothly shaped to follow a ...
Any geometric object can be used in a pencil. The common ones are lines, planes, circles, conics, spheres, and general curves. Even points can be used. A pencil of points is the set of all points on a given line. [1] A more common term for this set is a range of points.
SolveSpace supports parametric 2D drawing of lines, circles, arcs, cubic bézier curves etc; datum points and lines are also supported for general, reference based modeling. [13] 3D solid modeling Drawing, extrusion, rotation and revolution along a helix are supported in both modes.
In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features.
Supporting lines and tangent lines are not the same thing, [11] but for convex curves, every tangent line is a supporting line. [8] At a point of a curve where a tangent line exists, there can only be one supporting line, the tangent line. [12] Therefore, a smooth curve is convex if it lies on one side of each of its tangent lines.
In these figures, the red curves are the lines of curvature for one family of principal directions, and the blue curves for the other. When a line of curvature has a local extremum of the same principal curvature then the curve has a ridge point. These ridge points form curves on the surface called ridges. The ridge curves pass through the ...