Silverlight Custom Panels Part II : Fermat Spiral Panel

This next panel demonstrates that truly any mathematical algorithm can be leveraged to efficiently produce custom layout logic. In this case rather than using the boring old circular panel trick I thought I would pick a new algorithm to see what its affect was. I chose Fermat’s Spiral. Fermat’s spiral takes in two parameters: a radius and an angle.

fermat4

fermat5

Taken straight from Wikipedia, the source of all truth known to man [sic], where theta is the angle, r is the radius or distance from the center, n is the index number of the floret and c is a constant scaling factor. The constant that you see, 137.508, dubbed the “golden angle”, is actually one of those magically numbers in math whose meaning I don’t fully understand.

In my C# implementation below, I am mapping a property “Scalar” in for c, the index of this element in for n, and a property “Angle” in for the golden angle just to spice things up.

        protected override Size ArrangeOverride(Size finalSize)
        {
            int index = 0;
            foreach (UIElement child in this.Children)
            {
                double goldenAngle = 137.5;

                double r = Scalar * Math.Sqrt(index);
                double theta = index * Angle; // in degrees

                double centerX = (finalSize.Width / 2) - (CalculateAverageItemWidth()/2); // ?
                double centerY = (finalSize.Height /2) - (CalculateAverageItemHeight()/2); // ?
                
                double x = centerX + r * Math.Cos(theta);
                double y = centerY + r * Math.Sin(theta);

                Rect childRect = new Rect();

                child.Measure(finalSize);
                if (_firstArrange)
                {
                    childRect.X = 0;
                    childRect.Y = 1500;
                    childRect.Width = child.DesiredSize.Width;
                    childRect.Height = child.DesiredSize.Height;
                }
                else
                {
                    childRect.X = x;
                    childRect.Y = y;
                    childRect.Width = child.DesiredSize.Width;
                    childRect.Height = child.DesiredSize.Height;
                }
                child.Arrange(childRect); 
                if (_firstArrange && this.Children.Count > 0)
                {
                    _firstArrange = false;
                    this.InvalidateMeasure();
                }

                index++;
            }
            return base.ArrangeOverride(finalSize);
        }

 

Here are a few of my favorite configurations of this panel:

The “Archemedian”

Angle = 119.7

fermat1

The “Wave”

Angle = 72.1

fermat2

The “3 Way”

Angle = 60.67

fermat3

There are literally millions of different configurations of Fermat’s spiral. So have some fun and start tinkering!

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