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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 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 ...
The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6]
Line; Degree 2 Plane curves of ... Bring's curve (genus 4) Macbeath surface (genus 7) Butterfly curve (algebraic) (genus 7) Curve families with variable genus ...
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]
Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes.
A symmetry group in frieze group 1, 2, 3, or 5 is a subgroup of a symmetry group in the last frieze group with the same translational distance. A symmetry group in frieze group 4 or 6 is a subgroup of a symmetry group in the last frieze group with half the translational distance. This last frieze group contains the symmetry groups of the ...
This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...
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