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A Bézier curve is defined by a set of control points P0 through Pn, where n is called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the curve; however, the intermediate control points generally do not lie on the curve.
A Lissajous figure, made by releasing sand from a container at the end of a Blackburn pendulum. A Lissajous curve / ˈlɪsəʒuː /, also known as Lissajous figure or Bowditch curve / ˈbaʊdɪtʃ /, is the graph of a system of parametric equations. sin t + {\displaystyle x=A\sin (at+\delta ),\quad y=B\sin (bt),} which describe the ...
The variation diminishing property of Bézier curves is that they are smoother than the polygon formed by their control points. If a line is drawn through the curve, the number of intersections with the curve will be less than or equal to the number of intersections with the control polygon. In other words, for a Bézier curve B defined by the ...
Paul de Casteljau (19 November 1930 – 24 March 2022) was a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, leading to the curves widely known as Bézier curves.
Bernstein polynomials approximating a curve. In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician Sergei Natanovich Bernstein.
There are infinitely many different Lissajous knots, [4] and other examples with 10 or fewer crossings include the 7 4 knot, the 8 15 knot, the 10 1 knot, the 10 35 knot, the 10 58 knot, and the composite knot 5 2 * # 5 2, [1] as well as the 9 16 knot, 10 76 knot, the 10 99 knot, the 10 122 knot, the 10 144 knot, the granny knot, and the composite knot 5 2 # 5 2. [5]
Astrodynamics. In orbital mechanics, a Lissajous orbit (pronounced [li.sa.ʒu]), named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system with minimal propulsion. Lyapunov orbits around a Lagrangian point are curved paths that lie entirely in the plane ...
Thin paper discs containing an antibiotic have been placed on an agar plate growing bacteria. Bacteria are not able to grow around antibiotics to which they are sensitive. This is called "the zone of inhibition". Antibiotic sensitivity testing or antibiotic susceptibility testing is the measurement of the susceptibility of bacteria to antibiotics.