incircle-visualization

Computational Geometry inCircle Test Visualization

Purpose

Provide an interactive and visual learning experience for the inCircle Test. Users will fully understand what happens at each step of the inCircle Test. The application determines if the point q lies inside or outside the circle defined by the three points u, p, and v in the plane (figure1). The InCircle Test is being used as part of the Delaunay Triangulations to test wether an edge is Locally delaunay or not. They will see how lifting objects into the next dimension alters the appearance of the object.

Description

• Users will initially be asked to click (select) 4 total points in space. Three of the points will be used to draw the circle and we will determine if the other is inside or outside the circle. Screenshot2 shows what the user will see when selecting the points. Once the user has selected the points, they will press enter to continue the inCircle Test.
• Given the first three points, we will draw a triangle and find the circumcircle of that triangle to draw the circle. That circle will then be lifted up on those three points to R3 (red lines). Using these lifted points we will find the plane that passes through them and find its Norm (gradiant). An ellipse will be drawn with the lifted points. A paraboloid will then be drawn through the projected ellipse in the R3.
• The fourth and final point will then be lifted to R3 (green line). If it lies above the plane, then it is not inside the circle. If it is below the plane, it is in the circle.

Note

• Rotating the ellipse in R3 according to the plane shown in screen shot #4.
• Drawing the paraboloid
• The ability to move the points dynamically by user