Wednesday, October 22, 2008

Silverlight Eyes (Seyes) : eyes follow the mouse in Silverlight (aka xeyes)

Silverlight Eyes (Seyes) watches what you do and reports it to the Boss:

Silverligh Eyes

This code uses two main mechanism to achieve the effect

  1. It uses Polar coordinates to calculate where the focal point is relative to the centre of each eyeball. (Often the problem people look for as finding the angle between two points). The code uses the angle to calculate what direction the pupil should be facing, and uses the radius (or distance) to proportionally move the pupil away from the centre.

  2. It uses clipping to ensure that the pupil is always within the eye ball, which is accomplished by grouping the shapes into a canvas with a clipping region the same size of the eyeball.

The code also allows the user to visualize the calculations taking place by checking/unchecking the checkbox in the top left hand corner. Checking this shows the focal point, the lines of sight from each eye and the key values at the top (angle, distance, start point, end point)

There are a number of implementations of eye movement on the web, however a lot of them do not proportionally move the pupil away from the centre, this means the pupil in these animations are generally stuck at the edge of the eye. If you play with the application you will see that a proportional movement is more realistic - human brains are very good at calculating what other people are looking at based on the pupil positions.

Clipping can be seen in this picture:

The Xaml is as expected with the complication of grouping the parts of the eye together using a Canvas, with a Canvas.Clip to stop drawing outside of the eyeball:
<UserControl x:Class="Eyes.Page"
<Canvas x:Name="LayoutRoot" Background="White" MouseMove="LayoutRoot_MouseMove" Cursor="Arrow">
<TextBlock Name="TextDebug" Canvas.Left="10" Canvas.Top="0" Width="1000" Height="100" />
<CheckBox Name="ShowCalculation" Canvas.Left="0" Canvas.Top="0"
Checked="CheckBox_Changed" Unchecked="CheckBox_Changed" Canvas.ZIndex="7"

<Ellipse Canvas.Left="300" Canvas.Top="100" Width="230" Height="300" Stroke="Black" Name="Face" Fill="WhiteSmoke" Canvas.ZIndex="1"/>

<Canvas Canvas.Left="340" Canvas.Top="200" Canvas.ZIndex="2" >
<Ellipse Canvas.Left="0" Canvas.Top="0" Width="60" Height="40" Stroke="Black" Name="LeftEye" Fill="White" Canvas.ZIndex="2" />
<Ellipse Canvas.Left="10" Canvas.Top="10" Width="20" Height="20" Fill="Green" Name="LeftPupil" Canvas.ZIndex="2" />
<EllipseGeometry Center="30,20" RadiusX="30" RadiusY="20" />

<Canvas Canvas.Left="420" Canvas.Top="200" Canvas.ZIndex="2" >
<Ellipse Canvas.Left="0" Canvas.Top="0" Width="60" Height="40" Stroke="Black" Name="RightEye" Fill="White" Canvas.ZIndex="2" />
<Ellipse Canvas.Left="10" Canvas.Top="10" Width="20" Height="20" Fill="Green" Name="RightPupil" Canvas.ZIndex="2" />
<EllipseGeometry Center="30,20" RadiusX="30" RadiusY="20" />

<Ellipse Canvas.Left="395" Canvas.Top="270" Width="30" Height="40" Stroke="Black" Name="Nose" Fill="DarkGray" Canvas.ZIndex="1"/>

<Ellipse Canvas.Left="380" Canvas.Top="320" Width="60" Height="30" Stroke="Black" Name="Mouth" Fill="DarkGray" Canvas.ZIndex="1"/>

<Ellipse Canvas.Left="10" Canvas.Top="60" Width="10" Height="10" Fill="Red" Name="FocusPoint" Canvas.ZIndex="6" />
<Line Stroke="Red" Name="LineSightLeft" Canvas.ZIndex="5" StrokeDashArray="2 5" />
<Line Stroke="Red" Name="LineSightRight" Canvas.ZIndex="5" StrokeDashArray="2 5" />

The code behind simply responds to the mouse moving, for each eye calculates the polar coordinates and then moves the eyeball proportionally towards the mouse:

public partial class Page : UserControl
bool showCalcs;

public Page()

// default to showing calculations
ShowCalculation.IsChecked = this.showCalcs = true;

private void LayoutRoot_MouseMove(object sender, MouseEventArgs e)
// update UI based on cursor location
Point cursorPoint = e.GetPosition(LayoutRoot);


private void UpdateUI(Point cursorPoint)
// calculate the location of the focus based using the center of the circle
Point centerPoint = new Point(cursorPoint.X, cursorPoint.Y);

if (this.showCalcs)
FocusPoint.PointSet(new Point(cursorPoint.X - (FocusPoint.Width / 2), cursorPoint.Y - (FocusPoint.Height / 2)));

// focus eyes on point
FocusEye(centerPoint, LeftEye, LeftPupil, LineSightLeft);
FocusEye(centerPoint, RightEye, RightPupil, LineSightRight);

private void FocusEye(Point pointFocus, Ellipse eye, Ellipse pupil, Line sight)
// the centre of the eye needs to be converted to a global coordinate
// which it's parent has
Point pointStart = new Point(eye.Parent.PointGet().X + (eye.Width / 2), eye.Parent.PointGet().Y + (eye.Height / 2));
Point pointEnd = pointFocus;

// cartesian to polar conversion
double angle = Trigonometry.CalculateAngleInDegreesBetween(pointStart, pointEnd);
double distance = Trigonometry.CalculateDistanceBetween(pointStart, pointEnd);

if (this.showCalcs)
TextDebug.Text = String.Format(" {2:N1}deg {3:N1} {0} {1}", new object[] { pointStart, pointEnd, angle, distance });

// maximum focal distance
const double MAX_DISTANCE = 500d;

// the eye will move away from the center
// of the eye ball proportionally to its maxim view
// reduced by π to keep some of it visible
double pupilDistance = (eye.Width / Math.PI) * (distance / MAX_DISTANCE);

// polar to cartesian conversion
Point pointPupilOffset = Trigonometry.ConvertPolarToPoint(pupilDistance, angle);

// adjust for centre of eyeball and pupil
Point pupilLocation = new Point(
(eye.Width / 2) + pointPupilOffset.X - (pupil.Width / 2),
(eye.Height / 2) - pointPupilOffset.Y - (pupil.Height / 2));


if (this.showCalcs)
sight.X1 = pointStart.X;
sight.Y1 = pointStart.Y;
sight.X2 = pointEnd.X;
sight.Y2 = pointEnd.Y;

private void CheckBox_Changed(object sender, RoutedEventArgs e)
// show calculations visually
this.showCalcs = ShowCalculation.IsChecked ?? false;

Visibility visibility = (this.showCalcs) ? Visibility.Visible : Visibility.Collapsed;

FocusPoint.Visibility = visibility;
LineSightLeft.Visibility = visibility;
LineSightRight.Visibility = visibility;
TextDebug.Visibility = visibility;

if (this.showCalcs)
LayoutRoot.Cursor = Cursors.None;
LayoutRoot.Cursor = Cursors.Arrow;

The code uses some extension methods, as I started doing in my previous blog entry:

public static class XamlExtensions
public static Point PointGet(this DependencyObject sobj)
Point point = new Point((double)sobj.GetValue(Canvas.LeftProperty), (double)sobj.GetValue(Canvas.TopProperty));

return point;

public static void PointSet(this DependencyObject shape, Point newLocation)
shape.SetValue(Canvas.LeftProperty, newLocation.X);
shape.SetValue(Canvas.TopProperty, newLocation.Y);

public static Point GetCenterPoint(this Shape shape)
Point location = shape.PointGet();

Point centerPoint = new Point(location.X + (shape.Width / 2), location.Y + (shape.Height / 2));

return centerPoint;

and a helper class for doing the trig:

public class Trigonometry
public static double DegreesToRadians(double angle)
return ((angle * Math.PI) / 180f);

public static double RadiansToDegrees(double angle)
return ((angle * 180) / Math.PI);

public static double CalculateAngleInDegreesBetween(Point pointStart, Point pointEnd)
// difference between points on Y-Axis
// Silverlight Y axis needs to be inverted of cartesian coordinates
double dy = -(pointEnd.Y - pointStart.Y);
// difference between points on X-Axis
double dx = (pointEnd.X - pointStart.X);

// angle of the vector defined by dy, dx
double angleRadians = Math.Atan2(dy, dx);

// results in (-π,π], which needs mapping to [0,2π) by adding 2π to negative
if (angleRadians < 0)
angleRadians += 2 * Math.PI;

double angleDegrees = RadiansToDegrees(angleRadians);

return angleDegrees;

public static double CalculateDistanceBetween(Point pointStart, Point pointEnd)
double dySquared = Math.Pow(pointEnd.Y - pointStart.Y, 2);
double dxSquared = Math.Pow(pointEnd.X - pointStart.X, 2);

double distance = Math.Sqrt(dySquared + dxSquared);

return distance;

internal static Point ConvertPolarToPoint(double radius, double angleDegrees)
double angleRadians = DegreesToRadians(angleDegrees);

double x = radius * Math.Cos(angleRadians);
double y = radius * Math.Sin(angleRadians);

return new Point(x, y);

1 comment:

John Hamm said...

Very well-written and explained. Thanks for taking the time to write this, definitely going to use your trigonometry helpers. Looking forward to more trigonometry-based silverlight examples.