/// <summary>
/// Calculates the determinant of two vectors.
/// </summary>
/// <param name="vector1">The first vector to evaluate.</param>
/// <param name="vector2">The second vector to evaluate.</param>
/// <returns>The determinant of vector1 and vector2.</returns>
public static float Determinant(VectorF vector1, VectorF vector2)
{
// In the case of two 2D vectors, the determinant is the cross-product.
return CrossProduct(vector1, vector2);
}
/// <summary>
/// Retrieves the angle, expressed in radians, between the two specified vectors.
/// </summary>
/// <param name="vector1">The first vector to evaluate.</param>
/// <param name="vector2">The second vector to evaluate.</param>
/// <returns>The angle, in radians, between vector1 and vector2.</returns>
public static float AngleBetween(VectorF vector1, VectorF vector2)
{
vector1.Normalize();
vector2.Normalize();
double angle = Math.Atan2(vector2.y, vector2.x) - Math.Atan2(vector1.y, vector1.x);
if (angle > Math.PI)
{
angle -= Math.PI * 2.0;
}
else if (angle < -Math.PI)
{
angle += Math.PI * 2.0;
}
return (float)angle;
}
/// <summary>
/// Calculates the dot product of the two specified vectors and returns the result.
/// </summary>
/// <param name="vector1">The first vector to multiply.</param>
/// <param name="vector2">The second vector structure to multiply.</param>
/// <returns>The scalar dot product of vector1 and vector2, which is calculated
/// using the following formula: (vector1.X * vector2.X) + (vector1.Y * vector2.Y)</returns>
public static float Multiply(VectorF vector1, VectorF vector2)
{
return vector1 * vector2;
}
/// <summary>
/// Calculates the cross product of two vectors.
/// </summary>
/// <param name="vector1">The first vector to evaluate.</param>
/// <param name="vector2">The second vector to evaluate.</param>
/// <returns>The cross product of vector1 and vector2. The following formula is used to
/// calculate the cross product: (Vector1.X * Vector2.Y) - (Vector1.Y * Vector2.X)</returns>
public static float CrossProduct(VectorF vector1, VectorF vector2)
{
return (vector1.x * vector2.y) - (vector1.y * vector2.x);
}
/// <summary>
/// Multiplies the specified scalar by the specified vector and returns the resulting vector.
/// </summary>
/// <param name="vector">The vector to multiply.</param>
/// <param name="scalar">The scalar to multiply.</param>
/// <returns>The result of multiplying scalar and vector.</returns>
public static VectorF Multiply(VectorF vector, float scalar)
{
return vector * scalar;
}
/// <summary>
/// Divides the specified vector by the specified scalar and returns the result.
/// </summary>
/// <param name="vector">The vector structure to divide.</param>
/// <param name="scalar">The amount by which vector is divided.</param>
/// <returns>The result of dividing vector by scalar.</returns>
public static VectorF Divide(VectorF vector, float scalar)
{
return vector / scalar;
}
/// <summary>
/// Subtracts the specified vector from another specified vector.
/// </summary>
/// <param name="vector1">The vector from which vector2 is subtracted.</param>
/// <param name="vector2">The vector to subtract from vector1.</param>
/// <returns>The difference between vector1 and vector2.</returns>
public static VectorF Subtract(VectorF vector1, VectorF vector2)
{
return vector1 - vector2;
}
/// <summary>
/// Multiplies the specified scalar by the specified vector and returns the resulting vector.
/// </summary>
/// <param name="scalar">The scalar to multiply.</param>
/// <param name="vector">The vector to multiply.</param>
/// <returns>The result of multiplying scalar and vector.</returns>
public static VectorF Multiply(float scalar, VectorF vector)
{
return scalar * vector;
}
/// <summary>
/// Adds two vectors and returns the result.
/// </summary>
/// <param name="vector1">The first vector to add.</param>
/// <param name="vector2">The second vector to add.</param>
/// <returns> The sum of vector1 and vector2.</returns>
public static VectorF Add(VectorF vector1, VectorF vector2)
{
return vector1 + vector2;
}
/// <summary>
/// Translates the specified point by the specified vector and returns the resulting point.
/// </summary>
/// <param name="vector">The amount to translate the specified point.</param>
/// <param name="point">The point to translate.</param>
/// <returns>The result of translating point by vector.</returns>
public static PointF Add(VectorF vector, PointF point)
{
return vector + point;
}
/// <summary>
/// Compares two vectors for equality.
/// </summary>
/// <param name="value">The vector to compare with this vector.</param>
/// <returns>true if value has the same X and Y values as this vector;
/// otherwise, false.</returns>
public bool Equals(VectorF value)
{
return value == this;
}
/// <summary>
/// Compares the two specified vectors for equality.
/// </summary>
/// <param name="vector1">The first vector to compare.</param>
/// <param name="vector2">The second vector to compare.</param>
/// <returns>true if the X and Y components of vector1 and vector2 are equal;
/// otherwise, false.</returns>
public static bool Equals(VectorF vector1, VectorF vector2)
{
return vector1 == vector2;
}
/// <summary>
/// Start the inertia processor in Surface screen space.
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void OnAffine2DManipulationCompleted(object sender, Manipulation2DCompletedEventArgs e)
{
if (inertiaProcessor != null)
{
inertiaProcessor.Delta -= OnAffine2DInertiaDelta;
inertiaProcessor.Completed -= OnAffine2DInertiaCompleted;
inertiaProcessor.Complete(stopwatch.Elapsed100Nanoseconds());
}
VectorF translation = new VectorF(e.Total.TranslationX, e.Total.TranslationY);
// Don't start inertia if the tranlation is less than roughly 1/8" regardless of velocity.
if (translation.Length < 96 / 8f)
{
return;
}
// Scroll in the opposite direction because a ScrollViewer moves with the touch.
VectorF initialVelocity = new VectorF(-e.Velocities.LinearVelocityX, -e.Velocities.LinearVelocityY);
// Check velocity.
if (initialVelocity.Length < FlickUtilities.MinimumFlickVelocity)
{
// If velocity is below this threshold ignore it.
return;
}
if (initialVelocity.Length >= FlickUtilities.MaximumFlickVelocity)
{
// If velocity is too large, reduce it to a reasonable value.
initialVelocity.Normalize();
initialVelocity = FlickUtilities.MaximumFlickVelocity * initialVelocity;
}
processInertia = true;
inertiaProcessor = new InertiaProcessor2D();
inertiaProcessor.Delta += OnAffine2DInertiaDelta;
inertiaProcessor.Completed += OnAffine2DInertiaCompleted;
inertiaProcessor.TranslationBehavior = new InertiaTranslationBehavior2D
{
DesiredDisplacement = ConvertFromVerticalValueToScreenSpace(VerticalViewportSize),
InitialVelocityX = initialVelocity.X * HorizontalViewportSize,
InitialVelocityY = initialVelocity.Y * VerticalViewportSize
};
inertiaProcessor.InitialOriginX = ConvertFromHorizontalValueToScreenSpace(horizontalScrollBarStateMachine.Value);
inertiaProcessor.InitialOriginY = ConvertFromVerticalValueToScreenSpace(verticalScrollBarStateMachine.Value);
}
/// <summary>
/// Start the flicking behavior.
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void OnAffine2DManipulationCompleted(object sender, Affine2DOperationCompletedEventArgs e)
{
if (inertiaProcessor != null)
{
inertiaProcessor.Affine2DInertiaDelta -= OnAffine2DInertiaDelta;
inertiaProcessor.Affine2DInertiaCompleted -= OnAffine2DInertiaCompleted;
inertiaProcessor = null;
}
// The Manipulations should all run in screen space so don't convert between spaces.
VectorF initialVelocity;
VectorF maxViewPortSize;
if (Orientation == Orientation.Horizontal)
{
initialVelocity = new VectorF(e.VelocityX, 0);
maxViewPortSize = new VectorF(numberOfPixelsInAxis * viewportSize, 0);
}
else
{
initialVelocity = new VectorF(0, e.VelocityY);
maxViewPortSize = new VectorF(0, numberOfPixelsInAxis * viewportSize);
}
// Check velocity.
if (initialVelocity.Length < FlickUtilities.MinimumFlickVelocity)
{
return;
}
if (initialVelocity.Length >= MaximumFlickVelocity)
{
// If velocity is too large, reduce it to a reasonable value.
initialVelocity.Normalize();
initialVelocity = MaximumFlickVelocity * initialVelocity;
}
VectorF flickDistance;
if (FlickUtilities.TryGetFlickDistance(initialVelocity, out flickDistance, maxViewPortSize))
{
processInertia = true;
inertiaProcessor = new Affine2DInertiaProcessor();
inertiaProcessor.Affine2DInertiaDelta += OnAffine2DInertiaDelta;
inertiaProcessor.Affine2DInertiaCompleted += OnAffine2DInertiaCompleted;
float displacement = 0;
if (flickDistance.X == 0)
{
displacement = flickDistance.Y;
}
else if (flickDistance.Y == 0)
{
displacement = flickDistance.X;
}
else
{
displacement = Math.Min(flickDistance.X, flickDistance.Y);
}
inertiaProcessor.DesiredDisplacement = float.IsInfinity(displacement) ? 0 : Math.Abs(displacement);
inertiaProcessor.InitialTimestamp = stopwatch.ElapsedTicks;
inertiaProcessor.InitialVelocityX = initialVelocity.X;
inertiaProcessor.InitialVelocityY = initialVelocity.Y;
inertiaProcessor.InitialOriginX = ToScreenSpace(Value);
inertiaProcessor.InitialOriginY = ToScreenSpace(Value);
}
}
/// <summary>
/// Calculates the page size for a flick with a given velocity.
/// The method chooses vertical or horizontal direction depending on the
/// given initial velocity.
/// </summary>
/// <param name="velocity">flick velocity in device independent units per msec.</param>
/// <param name="flickDistance">flick page size in device independent units.</param>
/// <param name="maxViewportSize">The maximum size of the viewport.</param>
/// <returns></returns>
public static bool TryGetFlickDistance(VectorF velocity, out VectorF flickDistance, VectorF maxViewportSize)
{
Debug.Assert(!float.IsNaN(velocity.X) && !float.IsInfinity(velocity.X), "Cannot start flick with invalid velocity.X");
Debug.Assert(!float.IsNaN(velocity.Y) && !float.IsInfinity(velocity.Y), "Cannot start flick with invalid velocity.Y");
// Set the flickDistance to the maximum viewport size.
flickDistance = maxViewportSize;
// choose the main direction of the flick based on duration
float durationX = float.PositiveInfinity;
float durationY = float.PositiveInfinity;
if (Math.Abs(velocity.X) > float.Epsilon && !float.IsInfinity(flickDistance.X))
{
durationX = GetDurationGivenDistanceAndVelocity(flickDistance.X, velocity.X);
}
if (Math.Abs(velocity.Y) > float.Epsilon && !float.IsInfinity(flickDistance.Y))
{
durationY = GetDurationGivenDistanceAndVelocity(flickDistance.Y, velocity.Y);
}
// choose the minimum duration
float duration = Math.Min(durationX, durationY);
if (float.IsInfinity(duration))
{
// cannot calculate flick page size
return false;
}
// make sure that duration doesn't exceed MaximumFlickDuration,
if (duration > MaximumFlickDuration)
{
// recalculate duration for the 'flick' direction
if (durationX <= durationY)
{
// calculate deceleration based on X page size and MaximumFlickDuration
Debug.Assert(flickDistance.X > 0);
float deceleration = GetDecelerationGivenDistanceAndDuration(flickDistance.X, MaximumFlickDuration);
duration = GetDurationGivenVelocityAndDeceleration(velocity.X, deceleration);
}
else
{
// calculate deceleration based on Y page size and MaximumFlickDuration
Debug.Assert(flickDistance.Y > 0);
float deceleration = GetDecelerationGivenDistanceAndDuration(flickDistance.Y, MaximumFlickDuration);
duration = GetDurationGivenVelocityAndDeceleration(velocity.Y, deceleration);
}
Debug.Assert(duration <= MaximumFlickDuration, "Duration is supposed to be less than MaximumFlickDuration.");
}
// adjust the flick distance
if (duration < durationX)
{
flickDistance.X = Math.Abs(GetDistanceGivenVelocityAndDuration(velocity.X, duration));
}
if (duration < durationY)
{
flickDistance.Y = Math.Abs(GetDistanceGivenVelocityAndDuration(velocity.Y, duration));
}
return true;
}
