// TODO: could probably figure out "inverse" from direction of topY compared to bottomY
public static Vector3[] GetConeFrustumVertices(CSGCircleDefinition definition, float topHeight, float rotation, int segments, ref Vector3[] vertices, bool inverse = false)
{
var rotate = Quaternion.AngleAxis(rotation, Vector3.up);
var bottomAxisX = rotate * Vector3.right * definition.diameterX * 0.5f;
var bottomAxisZ = rotate * Vector3.forward * definition.diameterZ * 0.5f;
var topY = Vector3.up * topHeight;
var bottomY = Vector3.up * definition.height;
if (vertices == null ||
vertices.Length != segments + 1)
{
vertices = new Vector3[segments + 1];
}
float angleOffset = ((segments & 1) == 1) ? 0.0f : ((360.0f / segments) * 0.5f);
vertices[0] = topY;
for (int v = 0; v < segments; v++)
{
var r = (((v * 360.0f) / (float)segments) + angleOffset) * Mathf.Deg2Rad;
var s = Mathf.Sin(r);
var c = Mathf.Cos(r);
var bottomVertex = (bottomAxisX * c) + (bottomAxisZ * s);
bottomVertex += bottomY;
var vi = inverse ? (segments - v) : (v + 1);
vertices[vi] = bottomVertex;
}
return(vertices);
}
public static Vector2 Rotate(Vector2 v, float rad)
{
float cos = Mathf.Cos(rad);
float sin = Mathf.Sin(rad);
return(new Vector2(cos * v.x - sin * v.y, sin * v.x + cos * v.y));
}
public static void CreateSphereVertices(Vector3 diameterXYZ, float offsetY, bool generateFromCenter, int horzSegments, int vertSegments, ref Vector3[] vertices)
{
//var lastVertSegment = vertSegments - 1;
int vertexCount = (horzSegments * (vertSegments - 1)) + 2;
if (vertices == null ||
vertices.Length != vertexCount)
{
vertices = new Vector3[vertexCount];
}
var radius = 0.5f * diameterXYZ;
var offset = generateFromCenter ? offsetY : radius.y + offsetY;
vertices[0] = Vector3.down * radius.y;
vertices[1] = Vector3.up * radius.y;
vertices[0].y += offset;
vertices[1].y += offset;
// TODO: optimize
var degreePerSegment = (360.0f / horzSegments) * Mathf.Deg2Rad;
var angleOffset = ((horzSegments & 1) == 1) ? 0.0f : ((360.0f / horzSegments) * 0.5f) * Mathf.Deg2Rad;
for (int v = 1, vertexIndex = 2; v < vertSegments; v++)
{
var segmentFactor = ((v - (vertSegments / 2.0f)) / vertSegments); // [-0.5f ... 0.5f]
var segmentDegree = (segmentFactor * 180); // [-90 .. 90]
var segmentHeight = Mathf.Sin(segmentDegree * Mathf.Deg2Rad);
var segmentRadius = Mathf.Cos(segmentDegree * Mathf.Deg2Rad); // [0 .. 0.707 .. 1 .. 0.707 .. 0]
var yRingPos = (segmentHeight * radius.y) + offset;
var xRingRadius = segmentRadius * radius.x;
var zRingRadius = segmentRadius * radius.z;
if (radius.y < 0)
{
for (int h = horzSegments - 1; h >= 0; h--, vertexIndex++)
{
var hRad = (h * degreePerSegment) + angleOffset;
vertices[vertexIndex] = new Vector3(Mathf.Cos(hRad) * segmentRadius * radius.x,
yRingPos,
Mathf.Sin(hRad) * segmentRadius * radius.z);
}
}
else
{
for (int h = 0; h < horzSegments; h++, vertexIndex++)
{
var hRad = (h * degreePerSegment) + angleOffset;
vertices[vertexIndex] = new Vector3(Mathf.Cos(hRad) * segmentRadius * radius.x,
yRingPos,
Mathf.Sin(hRad) * segmentRadius * radius.z);
}
}
}
}
/// <summary>
/// Modeled after the piecewise exponentially-damped sine wave:
/// y = (1/2)*sin(13pi/2*(2*x))*Math.Pow(2, 10 * ((2*x) - 1)) ; [0,0.5)
/// y = (1/2)*(sin(-13pi/2*((2x-1)+1))*Math.Pow(2,-10(2*x-1)) + 2) ; [0.5, 1]
/// </summary>
public static float ElasticEaseInOut(float p)
{
if (p < 0.5f)
{
return(0.5f * Math.Sin(13 * HALFPI * (2 * p)) * Math.Pow(2, 10 * ((2 * p) - 1)));
}
return(0.5f * (Math.Sin(-13 * HALFPI * ((2 * p - 1) + 1)) * Math.Pow(2, -10 * (2 * p - 1)) + 2));
}
/// <summary>
/// Modeled after the piecewise exponentially-damped sine wave:
/// y = (1/2)*sin(13pi/2*(2*x))*Math.Pow(2, 10 * ((2*x) - 1)) ; [0,0.5)
/// y = (1/2)*(sin(-13pi/2*((2x-1)+1))*Math.Pow(2,-10(2*x-1)) + 2) ; [0.5, 1]
/// </summary>
public static float EaseInOutElastic(this float This)
{
if (This < 0.5f)
{
return(0.5f * Math.Sin(13 * HalfPi * (2 * This)) * Math.Pow(2, 10 * (2 * This - 1)));
}
return(0.5f * (Math.Sin(-13 * HalfPi * (2 * This - 1 + 1)) * Math.Pow(2, -10 * (2 * This - 1)) + 2));
}
Vector3 RandomCircle(Vector3 center, float radius, float angle)
{
Vector3 pos = new Vector3(0, 0, 0);
pos.x = center.x + radius * Mathf.Sin(angle * Mathf.Deg2Rad);
pos.y = center.y + radius * Mathf.Cos(angle * Mathf.Deg2Rad);
pos.z = angle;
return(pos);
}
public static bool GenerateHemisphereVertices(Vector3 diameterXYZ, Matrix4x4 transform, int horzSegments, int vertSegments, ref Vector3[] vertices)
{
var bottomCap = true;
var topCap = false;
var extraVertices = ((!bottomCap) ? 1 : 0) + ((!topCap) ? 1 : 0);
var rings = (vertSegments) + (topCap ? 1 : 0);
var vertexCount = (horzSegments * rings) + extraVertices;
var topVertex = 0;
var bottomVertex = (!topCap) ? 1 : 0;
var radius = new Vector3(diameterXYZ.x * 0.5f,
diameterXYZ.y,
diameterXYZ.z * 0.5f);
if (vertices == null ||
vertices.Length != vertexCount)
{
vertices = new Vector3[vertexCount];
}
if (!topCap)
{
vertices[topVertex] = transform.MultiplyPoint(Vector3.up * radius.y); // top
}
if (!bottomCap)
{
vertices[bottomVertex] = transform.MultiplyPoint(Vector3.zero); // bottom
}
var degreePerSegment = (360.0f / horzSegments) * Mathf.Deg2Rad;
var angleOffset = ((horzSegments & 1) == 1) ? 0.0f : 0.5f * degreePerSegment;
var vertexIndex = extraVertices;
{
for (int h = 0; h < horzSegments; h++, vertexIndex++)
{
var hRad = (h * degreePerSegment) + angleOffset;
vertices[vertexIndex] = transform.MultiplyPoint(new Vector3(Mathf.Cos(hRad) * radius.x,
0.0f,
Mathf.Sin(hRad) * radius.z));
}
}
for (int v = 1; v < rings; v++)
{
var segmentFactor = ((v - (rings / 2.0f)) / rings) + 0.5f; // [0.0f ... 1.0f]
var segmentDegree = (segmentFactor * 90); // [0 .. 90]
var segmentHeight = Mathf.Sin(segmentDegree * Mathf.Deg2Rad) * radius.y;
var segmentRadius = Mathf.Cos(segmentDegree * Mathf.Deg2Rad); // [0 .. 0.707 .. 1 .. 0.707 .. 0]
for (int h = 0; h < horzSegments; h++, vertexIndex++)
{
vertices[vertexIndex].x = vertices[h + extraVertices].x * segmentRadius;
vertices[vertexIndex].y = segmentHeight;
vertices[vertexIndex].z = vertices[h + extraVertices].z * segmentRadius;
}
}
return(true);
}
public static UnityEngine.Vector2 Rotate(this UnityEngine.Vector2 v, float degrees)
{
float radians = degrees * Mathf.Deg2Rad;
float sin = Mathf.Sin(radians);
float cos = Mathf.Cos(radians);
float tx = v.x;
float ty = v.y;
return(new UnityEngine.Vector2(cos * tx - sin * ty, sin * tx + cos * ty));
}
/// <summary>
/// Modeled after the piecewise expoly-damped sine wave:
/// y = (1/2)*sin(13pi/2*(2*x))*Math.Pow(2, 10 * ((2*x) - 1)) ; [0,0.5)
/// y = (1/2)*(sin(-13pi/2*((2x-1)+1))*Math.Pow(2,-10(2*x-1)) + 2) ; [0.5, 1]
/// </summary>
internal static float EaseInOutElastic(float p)
{
if (p < 0.5f)
{
return(0.5f * Math.Sin(13 * HALFPI * (2 * p)) * Math.Pow(2, 10 * ((2 * p) - 1)));
}
else
{
return(0.5f * ((Math.Sin(-13 * HALFPI * (2 * p)) * Math.Pow(2, -10 * ((2 * p) - 1))) + 2));
}
}
/// <summary>
/// Modeled after the piecewise overshooting cubic function:
/// y = (1/2)*((2x)^3-(2x)*sin(2*x*pi)) ; [0, 0.5)
/// y = (1/2)*(1-((1-x)^3-(1-x)*sin((1-x)*pi))+1) ; [0.5, 1]
/// </summary>
public static float EaseInOutBack(this float This)
{
if (This < 0.5f)
{
var f = 2 * This;
return(0.5f * (f * f * f - f * Math.Sin(f * Pi)));
}
else
{
var f = 1 - (2 * This - 1);
return(0.5f * (1 - (f * f * f - f * Math.Sin(f * Pi))) + 0.5f);
}
}
/// <summary>
/// Modeled after the piecewise overshooting cubic function:
/// y = (1/2)*((2x)^3-(2x)*sin(2*x*pi)) ; [0, 0.5)
/// y = (1/2)*(1-((1-x)^3-(1-x)*sin((1-x)*pi))+1) ; [0.5, 1]
/// </summary>
public static float BackEaseInOut(float p)
{
if (p < 0.5f)
{
float f = 2 * p;
return(0.5f * (f * f * f - f * Math.Sin(f * Pi)));
}
else
{
float f = (1 - (2 * p - 1));
return(0.5f * (1 - (f * f * f - f * Math.Sin(f * Pi))) + 0.5f);
}
}
/// <summary>
/// Modeled after the piecewise overshooting cubic function:
/// y = (1/2)*((2x)^3-(2x)*sin(2*x*pi)) ; [0, 0.5)
/// y = (1/2)*(1-((1-x)^3-(1-x)*sin((1-x)*pi))+1) ; [0.5, 1]
/// </summary>
static internal float easeInOutBack(float p)
{
if (p < 0.5f)
{
float f = 2 * p;
return(0.5f * (f * f * f - f * Math.Sin(f * PI)));
}
else
{
float f = (1 - (2 * p - 1));
return(0.5f * (1 - (f * f * f - f * Math.Sin(f * PI))) + 0.5f);
}
}
/// <summary>
/// Modeled after the piecewise overshooting cubic function:
/// y = (1/2)*((2x)^3-(2x)*sin(2*x*pi)) ; [0, 0.5)
/// y = (1/2)*(1-((1-x)^3-(1-x)*sin((1-x)*pi))+1) ; [0.5, 1]
/// </summary>
internal static float EaseInOutBack(float p)
{
if (p < 0.5f)
{
float f = 2 * p;
return(0.5f * ((f * f * f) - (f * Math.Sin(f * PI))));
}
else
{
float f = 1 - ((2 * p) - 1);
return((0.5f * (1 - ((f * f * f) - (f * Math.Sin(f * PI))))) + 0.5f);
}
}
/** Clamps the velocity to the max speed and optionally the forwards direction.
* \param velocity Desired velocity of the character. In world units per second.
* \param maxSpeed Max speed of the character. In world units per second.
* \param slowdownFactor Value between 0 and 1 which determines how much slower the character should move than normal.
* Normally 1 but should go to 0 when the character approaches the end of the path.
* \param slowWhenNotFacingTarget Prevent the velocity from being too far away from the forward direction of the character
* and slow the character down if the desired velocity is not in the same direction as the forward vector.
* \param forward Forward direction of the character. Used together with the \a slowWhenNotFacingTarget parameter.
*
* Note that all vectors are 2D vectors, not 3D vectors.
*
* \returns The clamped velocity in world units per second.
*/
public static Vector2 ClampVelocity(Vector2 velocity, float maxSpeed, float slowdownFactor, bool slowWhenNotFacingTarget, Vector2 forward)
{
// Max speed to use for this frame
var currentMaxSpeed = maxSpeed * slowdownFactor;
// Check if the agent should slow down in case it is not facing the direction it wants to move in
if (slowWhenNotFacingTarget && (forward.x != 0 || forward.y != 0))
{
float currentSpeed;
var normalizedVelocity = VectorMath.Normalize(velocity.ToPFV2(), out currentSpeed);
float dot = Vector2.Dot(normalizedVelocity.ToUnityV2(), forward);
// Lower the speed when the character's forward direction is not pointing towards the desired velocity
// 1 when velocity is in the same direction as forward
// 0.2 when they point in the opposite directions
float directionSpeedFactor = Mathf.Clamp(dot + 0.707f, 0.2f, 1.0f);
currentMaxSpeed *= directionSpeedFactor;
currentSpeed = Mathf.Min(currentSpeed, currentMaxSpeed);
// Angle between the forwards direction of the character and our desired velocity
float angle = Mathf.Acos(Mathf.Clamp(dot, -1, 1));
// Clamp the angle to 20 degrees
// We cannot keep the velocity exactly in the forwards direction of the character
// because we use the rotation to determine in which direction to rotate and if
// the velocity would always be in the forwards direction of the character then
// the character would never rotate.
// Allow larger angles when near the end of the path to prevent oscillations.
angle = Mathf.Min(angle, (20f + 180f * (1 - slowdownFactor * slowdownFactor)) * Mathf.Deg2Rad);
float sin = Mathf.Sin(angle);
float cos = Mathf.Cos(angle);
// Determine if we should rotate clockwise or counter-clockwise to move towards the current velocity
sin *= Mathf.Sign(normalizedVelocity.x * forward.y - normalizedVelocity.y * forward.x);
// Rotate the #forward vector by #angle radians
// The rotation is done using an inlined rotation matrix.
// See https://en.wikipedia.org/wiki/Rotation_matrix
return(new Vector2(forward.x * cos + forward.y * sin, forward.y * cos - forward.x * sin) * currentSpeed);
}
else
{
return(Vector2.ClampMagnitude(velocity, currentMaxSpeed));
}
}
public static Vector3[] GetConicalFrustumVertices(CSGCircleDefinition bottom, CSGCircleDefinition top, float rotation, int segments, ref Vector3[] vertices)
{
if (top.height > bottom.height)
{
var temp = top; top = bottom; bottom = temp;
}
var rotate = Quaternion.AngleAxis(rotation, Vector3.up);
var topAxisX = rotate * Vector3.right * top.diameterX * 0.5f;
var topAxisZ = rotate * Vector3.forward * top.diameterZ * 0.5f;
var bottomAxisX = rotate * Vector3.right * bottom.diameterX * 0.5f;
var bottomAxisZ = rotate * Vector3.forward * bottom.diameterZ * 0.5f;
var topY = Vector3.up * top.height;
var bottomY = Vector3.up * bottom.height;
// TODO: handle situation where diameterX & diameterZ are 0 (only create one vertex)
if (vertices == null ||
vertices.Length != segments * 2)
{
vertices = new Vector3[segments * 2];
}
float angleOffset = ((segments & 1) == 1) ? 0.0f : ((360.0f / segments) * 0.5f);
for (int v = 0; v < segments; v++)
{
var r = (((v * 360.0f) / (float)segments) + angleOffset) * Mathf.Deg2Rad;
var s = Mathf.Sin(r);
var c = Mathf.Cos(r);
var topVertex = (topAxisX * c) + (topAxisZ * s);
var bottomVertex = (bottomAxisX * c) + (bottomAxisZ * s);
topVertex += topY;
bottomVertex += bottomY;
vertices[v] = topVertex;
vertices[v + segments] = bottomVertex;
}
return(vertices);
}
public void Validate()
{
if (surfaceDefinition == null)
{
surfaceDefinition = new ChiselSurfaceDefinition();
}
topDiameterX = Mathf.Abs(topDiameterX);
topDiameterZ = Mathf.Abs(topDiameterZ);
bottomDiameterX = Mathf.Abs(bottomDiameterX);
bottomDiameterZ = Mathf.Abs(bottomDiameterZ);
sides = Mathf.Max(3, sides);
if (surfaceDefinition.EnsureSize(2 + sides))
{
// Top plane
surfaceDefinition.surfaces[0].surfaceDescription.UV0 = UVMatrix.centered;
// Bottom plane
surfaceDefinition.surfaces[1].surfaceDescription.UV0 = UVMatrix.centered;
float radius = topDiameterX * 0.5f;
float angle = (360.0f / sides);
float sideLength = (2 * Mathf.Sin((angle / 2.0f) * Mathf.Deg2Rad)) * radius;
// Side planes
for (int i = 2; i < 2 + sides; i++)
{
var uv0 = UVMatrix.identity;
uv0.U.w = ((i - 2) + 0.5f) * sideLength;
// TODO: align with bottom
//uv0.V.w = 0.5f;
surfaceDefinition.surfaces[i].surfaceDescription.UV0 = uv0;
surfaceDefinition.surfaces[i].surfaceDescription.smoothingGroup = smoothingGroup;
}
}
}
/// <summary>
/// Modeled after quarter-cycle of sine wave (different phase)
/// </summary>
internal static float EaseOutSine(float p)
{
return(Math.Sin(p * HALFPI));
}
/// <summary>
/// Modeled after overshooting cubic y = 1-((1-x)^3-(1-x)*sin((1-x)*pi))
/// </summary>
public static float BackEaseOut(float p)
{
float f = (1 - p);
return(1 - (f * f * f - f * Math.Sin(f * Pi)));
}
/// <summary>
/// Modeled after the overshooting cubic y = x^3-x*sin(x*pi)
/// </summary>
public static float BackEaseIn(float p)
{
return(p * p * p - p * Math.Sin(p * Pi));
}
/// <summary>
/// Modeled after the damped sine wave y = sin(-13pi/2*(x + 1))*Math.Pow(2, -10x) + 1
/// </summary>
public static float ElasticEaseOut(float p)
{
return(Math.Sin(-13 * HalfPi * (p + 1)) * Math.Pow(2, -10 * p) + 1);
}
/// <summary>
/// Modeled after the damped sine wave y = sin(13pi/2*x)*Math.Pow(2, 10 * (x - 1))
/// </summary>
public static float ElasticEaseIn(float p)
{
return(Math.Sin(13 * HalfPi * p) * Math.Pow(2, 10 * (p - 1)));
}
/// <summary>
/// Modeled after quarter-cycle of sine wave (different phase)
/// </summary>
public static float SineEaseOut(float p)
{
return(Math.Sin(p * HalfPi));
}
/// <summary>
/// Modeled after quarter-cycle of sine wave
/// </summary>
public static float SineEaseIn(float p)
{
return(Math.Sin((p - 1) * HalfPi) + 1);
}
public static float ElasticIn(float p)
{
return(-(Mathf.Pow(2, 10 * (p - 1f)) * Mathf.Sin((p - 1.075f) * (Mathf.PI * 2) / 0.3f)));
}
// possible situations:
// capsule with top AND bottom set to >0 height
// capsule with top OR bottom set to 0 height
// capsule with both top AND bottom set to 0 height
// capsule with height equal to top and bottom height
public static bool GenerateCapsuleVertices(ref CSGCapsuleDefinition definition, ref Vector3[] vertices)
{
definition.Validate();
var haveTopHemisphere = definition.haveRoundedTop;
var haveBottomHemisphere = definition.haveRoundedBottom;
var haveMiddleCylinder = definition.haveCylinder;
if (!haveBottomHemisphere && !haveTopHemisphere && !haveMiddleCylinder)
{
return(false);
}
var radiusX = definition.diameterX * 0.5f;
var radiusZ = definition.diameterZ * 0.5f;
var topHeight = haveTopHemisphere ? definition.topHeight : 0;
var bottomHeight = haveBottomHemisphere ? definition.bottomHeight : 0;
var totalHeight = definition.height;
var cylinderHeight = definition.cylinderHeight;
var sides = definition.sides;
var extraVertices = definition.extraVertexCount;
var bottomRings = definition.bottomRingCount;
var topRings = definition.topRingCount;
var ringCount = definition.ringCount;
var vertexCount = definition.vertexCount;
var bottomVertex = definition.bottomVertex;
var topVertex = definition.topVertex;
var topOffset = definition.topOffset + definition.offsetY;
var bottomOffset = definition.bottomOffset + definition.offsetY;
if (vertices == null ||
vertices.Length != vertexCount)
{
vertices = new Vector3[vertexCount];
}
if (haveBottomHemisphere)
{
vertices[bottomVertex] = Vector3.up * (bottomOffset - bottomHeight); // bottom
}
if (haveTopHemisphere)
{
vertices[topVertex] = Vector3.up * (topOffset + topHeight); // top
}
var degreePerSegment = (360.0f / sides) * Mathf.Deg2Rad;
var angleOffset = definition.rotation + (((sides & 1) == 1) ? 0.0f : 0.5f * degreePerSegment);
var topVertexOffset = extraVertices + ((topRings - 1) * sides);
var bottomVertexOffset = extraVertices + ((ringCount - bottomRings) * sides);
var unitCircleOffset = topVertexOffset;
var vertexIndex = unitCircleOffset;
{
for (int h = sides - 1; h >= 0; h--, vertexIndex++)
{
var hRad = (h * degreePerSegment) + angleOffset;
vertices[vertexIndex] = new Vector3(Mathf.Cos(hRad) * radiusX,
0.0f,
Mathf.Sin(hRad) * radiusZ);
}
}
for (int v = 1; v < topRings; v++)
{
vertexIndex = topVertexOffset - (v * sides);
var segmentFactor = ((v - (topRings * 0.5f)) / topRings) + 0.5f; // [0.0f ... 1.0f]
var segmentDegree = (segmentFactor * 90); // [0 .. 90]
var segmentHeight = topOffset +
(Mathf.Sin(segmentDegree * Mathf.Deg2Rad) *
topHeight);
var segmentRadius = Mathf.Cos(segmentDegree * Mathf.Deg2Rad); // [0 .. 0.707 .. 1 .. 0.707 .. 0]
for (int h = 0; h < sides; h++, vertexIndex++)
{
vertices[vertexIndex].x = vertices[h + unitCircleOffset].x * segmentRadius;
vertices[vertexIndex].y = segmentHeight;
vertices[vertexIndex].z = vertices[h + unitCircleOffset].z * segmentRadius;
}
}
vertexIndex = bottomVertexOffset;
{
for (int h = 0; h < sides; h++, vertexIndex++)
{
vertices[vertexIndex] = new Vector3(vertices[h + unitCircleOffset].x,
bottomOffset,
vertices[h + unitCircleOffset].z);
}
}
for (int v = 1; v < bottomRings; v++)
{
var segmentFactor = ((v - (bottomRings * 0.5f)) / bottomRings) + 0.5f; // [0.0f ... 1.0f]
var segmentDegree = (segmentFactor * 90); // [0 .. 90]
var segmentHeight = bottomOffset - bottomHeight +
((1 - Mathf.Sin(segmentDegree * Mathf.Deg2Rad)) *
bottomHeight);
var segmentRadius = Mathf.Cos(segmentDegree * Mathf.Deg2Rad); // [0 .. 0.707 .. 1 .. 0.707 .. 0]
for (int h = 0; h < sides; h++, vertexIndex++)
{
vertices[vertexIndex].x = vertices[h + unitCircleOffset].x * segmentRadius;
vertices[vertexIndex].y = segmentHeight;
vertices[vertexIndex].z = vertices[h + unitCircleOffset].z * segmentRadius;
}
}
{
for (int h = 0; h < sides; h++, vertexIndex++)
{
vertices[h + unitCircleOffset].y = topOffset;
}
}
return(true);
}
/// <summary>
/// Modeled after overshooting cubic y = 1-((1-x)^3-(1-x)*sin((1-x)*pi))
/// </summary>
internal static float EaseOutBack(float p)
{
float f = 1 - p;
return(1 - ((f * f * f) - (f * Math.Sin(f * PI))));
}
/// <summary>
/// Modeled after the overshooting cubic y = x^3-x*sin(x*pi)
/// </summary>
internal static float EaseInBack(float p)
{
return((p * p * p) - (p * Math.Sin(p * PI)));
}
/// <summary>
/// Modeled after the damped sine wave y = sin(-13pi/2*(x + 1))*Math.Pow(2, -10x) + 1
/// </summary>
internal static float EaseOutElastic(float p)
{
return((Math.Sin(-13 * HALFPI * (p + 1)) * Math.Pow(2, -10 * p)) + 1);
}
/// <summary>
/// Modeled after the damped sine wave y = sin(13pi/2*x)*Math.Pow(2, 10 * (x - 1))
/// </summary>
internal static float EaseInElastic(float p)
{
return(Math.Sin(13 * HALFPI * p) * Math.Pow(2, 10 * (p - 1)));
}
/// <summary>
/// Modeled after quarter-cycle of sine wave
/// </summary>
internal static float EaseInSine(float p)
{
return(Math.Sin((p - 1) * HALFPI) + 1);
}