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A circle of radius 23 drawn by the Bresenham algorithm. In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. It is a generalization of Bresenham's line algorithm. The algorithm can be further generalized to conic sections. [1] [2] [3]
Example of the circle packing theorem on K − 5, the complete graph on five vertices, minus one edge. We say that two circles drawn in a plane kiss (or osculate) whenever they intersect in exactly one point. A "coin graph" is a graph formed by a set of circles, no two of which have overlapping interiors, by making a vertex for each circle and ...
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
Following the steps for drawing the Mohr circle for this particular state of stress, we first draw a Cartesian coordinate system (,) with the -axis upward. We then plot two points A(50,40) and B(-10,-40), representing the state of stress at plane A and B as show in both Figure 8 and Figure 9.
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a) 2 + (y − b) 2 = r 2 where a and b are the coordinates of the center (a, b) and r is the radius. In Cartesian geometry, equations are used to describe geometric figures.
The distance estimation can be used for drawing of the boundary of the Mandelbrot set, see the article Julia set. In this approach, pixels that are sufficiently close to M are drawn using a different color. This creates drawings where the thin "filaments" of the Mandelbrot set can be easily seen.
The isoperimetric inequality states that , and that the equality holds if and only if the curve is a circle. The area of a disk of radius R is πR 2 and the circumference of the circle is 2πR, so both sides of the inequality are equal to 4π 2 R 2 in this case.
The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ. For the tan function, the equation is: