How to determine shape is Semicircle by given point collection?

Question

Here is point collection of polygons

<Polygon Points="24,188,24,183,25,176,26,172,29,166,33,160,38,155,44,151,50,148,54,147,61,146,67,146,74,147,78,148,84,151,90,155,95,160,99,166,102,172,103,176,104,183,104,188" Stroke="Black" StrokeThickness="1" />
<Polygon Points="568,263,520,263,520,256,521,253,523,249,526,245,531,241,536,239,540,238,548,238,552,239,557,241,562,245,565,249,567,253,568,256,568,263" Stroke="Black" StrokeThickness="1" />

that gives me below shapes.

I need to check the shape is a semicircle or not? Please anyone can guide me to determine. Is it semicircle?

I will only get collection before drawing only I should determine the shapes. It can be any(Rectangle, Line, Semicircle, curve etc.)I am able to find a rectangle, triangle and lines shape from point collection. like for a rectangle, I am checking its opposite faces should be equal and inside angle should be 90 degrees.

  public bool IsRectangle()
        {                
            var pointColl = polygon.PointCollection;
            bool isRightAngle = false;

            if (polygon == null || pointColl == null)
            {
                return false;
            }
            if (pointColl.Count == 5)
            {
                double length1 = (pointColl[0] - pointColl[1]).LengthSquared;
                double width1 = (pointColl[1] - pointColl[2]).LengthSquared;
                double length2 = (pointColl[2] - pointColl[3]).LengthSquared;
                double width2 = (pointColl[3] - pointColl[0]).LengthSquared;

                if ((length1 == length2 && length1 != 0) && (width1 == width2 && width1 != 0))
                    isRightAngle = CalculateAngle(polygon);
            }
            else
            {
                isRightAngle = false;
            }

Can I write something like this for a semicircle or circular shape detection? Thanks in advance.

Answer 1

What defines a shape as being a semicircle?

In the true sense of the word, neither of your shapes are semi-circles as they are both composed of straight line segments.

How many points does a shape need to be considered as a semi-circle (is triangle sufficiently round enough). What is the margin of error of each point on the circumference (some percentage of the radius) before a shape is no longer considered to be semi-circular.

Some pseudo code for you ...

1. Given a collection of n points P1, P2 .. Pn
2. For each pair of points, calculate the distance between them.
3. The two points with the maximum distance between them (Pa & Pb) are considered to be the diameter (flat side) of the semi circle.
4. The centre point of the semi-circle is the mid point between Pa and Pb.
5. The distance from Pa & Pb to the centre point is radius R.
6. For each remaining point in the collection, calculate the distance to the centre point. If this distance lies within (1 +/- e) * R for all points, then the shape is a semi-circle. The value of e is left for you to define.

Note that this method will work whatever the orientation of the semi-circle. If you need something more specific then also check the slope of the line from Pa to Pb.

Answer 2

Algorithm:

1) Take 3 points from polygon.

2) Estimate circle from them using this method (or any other).

3) Check if other points from given poligon are placed on the estimated circle.