/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains cubic interpolation of the specified vectors.
/// </summary>
/// <param name="value1">Source <see cref="Vector2D"/>.</param>
/// <param name="value2">Source <see cref="Vector2D"/>.</param>
/// <param name="amount">Weighting value.</param>
/// <returns>Cubic interpolation of the specified vectors.</returns>
public static Vector2D SmoothStep(Vector2D value1, Vector2D value2, double amount)
{
return(new Vector2D(
MathHelperD.SmoothStep(value1.X, value2.X, amount),
MathHelperD.SmoothStep(value1.Y, value2.Y, amount)
));
}
/// <summary>
/// Clamps the specified value within a range.
/// </summary>
/// <param name="value1">The value to clamp.</param>
/// <param name="min">The min value.</param>
/// <param name="max">The max value.</param>
/// <returns>The clamped value.</returns>
public static Vector2D Clamp(Vector2D value1, Vector2D min, Vector2D max)
{
return(new Vector2D(
MathHelperD.Clamp(value1.X, min.X, max.X),
MathHelperD.Clamp(value1.Y, min.Y, max.Y)
));
}
/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains cubic interpolation of the specified vectors.
/// </summary>
/// <param name="value1">Source <see cref="Vector2D"/>.</param>
/// <param name="value2">Source <see cref="Vector2D"/>.</param>
/// <param name="amount">Weighting value.</param>
/// <param name="result">Cubic interpolation of the specified vectors as an output parameter.</param>
public static void SmoothStep(
ref Vector2D value1,
ref Vector2D value2,
double amount,
out Vector2D result
)
{
result.X = MathHelperD.SmoothStep(value1.X, value2.X, amount);
result.Y = MathHelperD.SmoothStep(value1.Y, value2.Y, amount);
}
/// <summary>
/// Clamps the specified value within a range.
/// </summary>
/// <param name="value1">The value to clamp.</param>
/// <param name="min">The min value.</param>
/// <param name="max">The max value.</param>
/// <param name="result">The clamped value as an output parameter.</param>
public static void Clamp(
ref Vector2D value1,
ref Vector2D min,
ref Vector2D max,
out Vector2D result
)
{
result.X = MathHelperD.Clamp(value1.X, min.X, max.X);
result.Y = MathHelperD.Clamp(value1.Y, min.Y, max.Y);
}
/// <summary>
/// Interpolates between two values using a cubic equation.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <param name="amount">Weighting value.</param>
/// <returns>Interpolated value.</returns>
public static double SmoothStep(double value1, double value2, double amount)
{
/* It is expected that 0 < amount < 1.
* If amount < 0, return value1.
* If amount > 1, return value2.
*/
double result = MathHelperD.Clamp(amount, 0f, 1f);
result = MathHelperD.Hermite(value1, 0f, value2, 0f, result);
return(result);
}
/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains hermite spline interpolation.
/// </summary>
/// <param name="value1">The first position vector.</param>
/// <param name="tangent1">The first tangent vector.</param>
/// <param name="value2">The second position vector.</param>
/// <param name="tangent2">The second tangent vector.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">The hermite spline interpolation vector as an output parameter.</param>
public static void Hermite(
ref Vector2D value1,
ref Vector2D tangent1,
ref Vector2D value2,
ref Vector2D tangent2,
double amount,
out Vector2D result
)
{
result.X = MathHelperD.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount);
result.Y = MathHelperD.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount);
}
/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains CatmullRom interpolation of the specified vectors.
/// </summary>
/// <param name="value1">The first vector in interpolation.</param>
/// <param name="value2">The second vector in interpolation.</param>
/// <param name="value3">The third vector in interpolation.</param>
/// <param name="value4">The fourth vector in interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">The result of CatmullRom interpolation as an output parameter.</param>
public static void CatmullRom(
ref Vector2D value1,
ref Vector2D value2,
ref Vector2D value3,
ref Vector2D value4,
double amount,
out Vector2D result
)
{
result.X = MathHelperD.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount);
result.Y = MathHelperD.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount);
}
/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 2d-triangle.
/// </summary>
/// <param name="value1">The first vector of 2d-triangle.</param>
/// <param name="value2">The second vector of 2d-triangle.</param>
/// <param name="value3">The third vector of 2d-triangle.</param>
/// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 2d-triangle.</param>
/// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 2d-triangle.</param>
/// <param name="result">The cartesian translation of barycentric coordinates as an output parameter.</param>
public static void Barycentric(
ref Vector2D value1,
ref Vector2D value2,
ref Vector2D value3,
double amount1,
double amount2,
out Vector2D result
)
{
result.X = MathHelperD.Barycentric(value1.X, value2.X, value3.X, amount1, amount2);
result.Y = MathHelperD.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2);
}
/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains CatmullRom interpolation of the specified vectors.
/// </summary>
/// <param name="value1">The first vector in interpolation.</param>
/// <param name="value2">The second vector in interpolation.</param>
/// <param name="value3">The third vector in interpolation.</param>
/// <param name="value4">The fourth vector in interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>The result of CatmullRom interpolation.</returns>
public static Vector2D CatmullRom(
Vector2D value1,
Vector2D value2,
Vector2D value3,
Vector2D value4,
double amount
)
{
return(new Vector2D(
MathHelperD.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
MathHelperD.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount)
));
}
/// <summary>
/// Creates a new <see cref="Vector2D"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 2d-triangle.
/// </summary>
/// <param name="value1">The first vector of 2d-triangle.</param>
/// <param name="value2">The second vector of 2d-triangle.</param>
/// <param name="value3">The third vector of 2d-triangle.</param>
/// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 2d-triangle.</param>
/// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 2d-triangle.</param>
/// <returns>The cartesian translation of barycentric coordinates.</returns>
public static Vector2D Barycentric(
Vector2D value1,
Vector2D value2,
Vector2D value3,
double amount1,
double amount2
)
{
return(new Vector2D(
MathHelperD.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
MathHelperD.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2)
));
}
private void UpdateVisibleArea()
{
var inverseViewMatrix = MatrixD.Invert(Transform);
var tl = Vector2D.Transform(Vector2D.Zero, inverseViewMatrix);
var tr = Vector2D.Transform(new Vector2D(Bounds.X, 0), inverseViewMatrix);
var bl = Vector2D.Transform(new Vector2D(0, Bounds.Y), inverseViewMatrix);
var br = Vector2D.Transform(new Vector2D(Bounds.Width, Bounds.Height), inverseViewMatrix);
var min = new Vector2D(
MathHelperD.Min(tl.X, MathHelperD.Min(tr.X, MathHelperD.Min(bl.X, br.X))),
MathHelperD.Min(tl.Y, MathHelperD.Min(tr.Y, MathHelperD.Min(bl.Y, br.Y))));
var max = new Vector2D(
MathHelperD.Max(tl.X, MathHelperD.Max(tr.X, MathHelperD.Max(bl.X, br.X))),
MathHelperD.Max(tl.Y, MathHelperD.Max(tr.Y, MathHelperD.Max(bl.Y, br.Y))));
VisibleArea = new RectangleD(min.X, min.Y, (max.X - min.X), (max.Y - min.Y));
}
// Adapted from http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-7-intersecting-simple-shapes/ray-box-intersection/
public double?Intersects(BoundingBoxD box)
{
double?tMin = null, tMax = null;
if (MathHelperD.WithinEpsilon(Direction.X, 0.0f))
{
if (Position.X < box.Min.X || Position.X > box.Max.X)
{
return(null);
}
}
else
{
tMin = (box.Min.X - Position.X) / Direction.X;
tMax = (box.Max.X - Position.X) / Direction.X;
if (tMin > tMax)
{
double?temp = tMin;
tMin = tMax;
tMax = temp;
}
}
if (MathHelperD.WithinEpsilon(Direction.Y, 0.0f))
{
if (Position.Y < box.Min.Y || Position.Y > box.Max.Y)
{
return(null);
}
}
else
{
double tMinY = (box.Min.Y - Position.Y) / Direction.Y;
double tMaxY = (box.Max.Y - Position.Y) / Direction.Y;
if (tMinY > tMaxY)
{
double temp = tMinY;
tMinY = tMaxY;
tMaxY = temp;
}
if ((tMin.HasValue && tMin > tMaxY) ||
(tMax.HasValue && tMinY > tMax))
{
return(null);
}
if (!tMin.HasValue || tMinY > tMin)
{
tMin = tMinY;
}
if (!tMax.HasValue || tMaxY < tMax)
{
tMax = tMaxY;
}
}
if (MathHelperD.WithinEpsilon(Direction.Z, 0.0f))
{
if (Position.Z < box.Min.Z || Position.Z > box.Max.Z)
{
return(null);
}
}
else
{
double tMinZ = (box.Min.Z - Position.Z) / Direction.Z;
double tMaxZ = (box.Max.Z - Position.Z) / Direction.Z;
if (tMinZ > tMaxZ)
{
double temp = tMinZ;
tMinZ = tMaxZ;
tMaxZ = temp;
}
if ((tMin.HasValue && tMin > tMaxZ) ||
(tMax.HasValue && tMinZ > tMax))
{
return(null);
}
if (!tMin.HasValue || tMinZ > tMin)
{
tMin = tMinZ;
}
if (!tMax.HasValue || tMaxZ < tMax)
{
tMax = tMaxZ;
}
}
/* Having a positive tMin and a negative tMax means the ray is inside the
* box we expect the intesection distance to be 0 in that case.
*/
if ((tMin.HasValue && tMin < 0) && tMax > 0)
{
return(0);
}
/* A negative tMin means that the intersection point is behind the ray's
* origin. We discard these as not hitting the AABB.
*/
if (tMin < 0)
{
return(null);
}
return(tMin);
}