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In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface.
The number of knots is always equal to the number of control points plus curve degree plus one (i.e. number of control points plus curve order). The knot vector divides the parametric space in the intervals mentioned before, usually referred to as knot spans. Each time the parameter value enters a new knot span, a new control point becomes ...
In topology and knot theory, the trefoil is usually defined using a knot diagram instead of an explicit parametric equation. In algebraic geometry, the trefoil can also be obtained as the intersection in C 2 of the unit 3-sphere S 3 with the complex plane curve of zeroes of the complex polynomial z 2 + w 3 (a cuspidal cubic).
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. [1] "
The Liang–Barsky algorithm uses the parametric equation of a line and inequalities describing the range of the clipping window to determine the intersections between the line and the clip window. With these intersections, it knows which portion of the line should be drawn. So this algorithm is significantly more efficient than Cohen–Sutherland
The first step is transforming the equation of a line from the typical slope-intercept form into something different; and then using this new equation to draw a line ...
The Fermat spiral with polar equation = can be converted to the Cartesian coordinates (x, y) by using the standard conversion formulas x = r cos φ and y = r sin φ.Using the polar equation for the spiral to eliminate r from these conversions produces parametric equations for one branch of the curve:
Here the parametric equation of a line in the view plane is = + where . Now to find the intersection point with the clipping window, we calculate the value of the dot product . Let p E {\displaystyle \mathbf {p} _{E}} be a point on the clipping plane E {\displaystyle E} .