Tag Archives: circles

Draw many circles that intersect two points in C#

As I mentioned in my earlier post Connect two points with elliptical arcs in C#, an infinite number of circles (or ellipses) can pass through two points. This example draws some of them to produce an interesting pattern. This example … Continue reading

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Connect two points with arcs of midpoint circles in C#

Two points alone cannot uniquely define a circle because an infinite number of circles can pass through two points and therefore they can be connected by an infinite number of arcs. If you add extra information, however, two points can … Continue reading

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Make an Apollonian gasket filled with images in C#

This example shows how to draw an Apollonian gasket filled with images of a cat. (I promise that this will be my last cat fractal for a while, although I may have one other cat image post coming up. ;-)) … Continue reading

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Draw an interesting pattern of circles in C#

This program simply draws an interesting arrangement of circles. I wrote it because a C# Helper post was mentioned on this Factal [sic] Patterns & Art page. This program uses the following code to draw the circles and connecting lines. … Continue reading

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Randomly color an Apollonian gasket in C#

This example is similar to the example Draw an Apollonian gasket in C# except it fills the circles it draws with random colors. The program uses the following code to generate random colors. // Return a random color. private Random … Continue reading

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Draw an Apollonian gasket in C#

The example Find circles that are tangent to three given circles (Apollonius’ Problem) in C# shows how to find up to eight circles that are tangent to three given circles. This example uses that method to build an Apollonian gasket. … Continue reading

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Draw three circles and find their tangent circles in C#

This example is similar to previous one Find circles that are tangent to three given circles (Apollonius’ Problem) in C# except it lets you click and drag to draw the three given circles. It then finds the (up to) 8 … Continue reading

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Find circles that are tangent to three given circles (Apollonius’ Problem) in C#

Given three objects that can be a point, line, or circle, you can try to draw circles that are tangent to each. The case using three circles is called Apollonius’ Problem. Originally these problems were studied by Euclid (ca. 300 … Continue reading

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Draw a circle through three points in C#

The perpendicular bisector of any chord on a circle passes through the circle’s center. To find the center given three points, simply find the perpendicular bisectors of the first two and last two pairs of points, and see where the … Continue reading

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Partition an area with circles and draw each region’s count in C#

This example shows how you can partition an area with circles and determine the number of circles that contain each of the pieces. The example Find the area where circles overlap in C# explains how to find the area where … Continue reading

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