public static XMVector RotationRollPitchYawFromVector(XMVector angles)
{
XMVector sign = XMVector.FromFloat(1.0f, -1.0f, -1.0f, 1.0f);
XMVector halfAngles = XMVector.Multiply(angles, XMGlobalConstants.OneHalf);
XMVector sinAngles;
XMVector cosAngles;
halfAngles.SinCos(out sinAngles, out cosAngles);
XMVector p0 = new XMVector(sinAngles.X, cosAngles.X, cosAngles.X, cosAngles.X);
XMVector y0 = new XMVector(cosAngles.Y, sinAngles.Y, cosAngles.Y, cosAngles.Y);
XMVector r0 = new XMVector(cosAngles.Z, cosAngles.Z, sinAngles.Z, cosAngles.Z);
XMVector p1 = new XMVector(cosAngles.X, sinAngles.X, sinAngles.X, sinAngles.X);
XMVector y1 = new XMVector(sinAngles.Y, cosAngles.Y, sinAngles.Y, sinAngles.Y);
XMVector r1 = new XMVector(sinAngles.Z, sinAngles.Z, cosAngles.Z, sinAngles.Z);
XMVector q1 = XMVector.Multiply(p1, sign);
XMVector q0 = XMVector.Multiply(p0, y0);
q1 = XMVector.Multiply(q1, y1);
q0 = XMVector.Multiply(q0, r0);
return(XMVector.MultiplyAdd(q1, r1, q0));
}
public static XMVector RefractV(XMVector incident, XMVector normal, XMVector refractionIndex)
{
//// Result = RefractionIndex * Incident - Normal * (RefractionIndex * dot(Incident, Normal) +
//// sqrt(1 - RefractionIndex * RefractionIndex * (1 - dot(Incident, Normal) * dot(Incident, Normal))))
XMVector zero = XMVector.Zero;
XMVector incidentDotNormal = XMVector4.Dot(incident, normal);
// R = 1.0f - RefractionIndex * RefractionIndex * (1.0f - IDotN * IDotN)
XMVector r = XMVector.NegativeMultiplySubtract(incidentDotNormal, incidentDotNormal, XMGlobalConstants.One);
r = XMVector.Multiply(r, refractionIndex);
r = XMVector.NegativeMultiplySubtract(r, refractionIndex, XMGlobalConstants.One);
if (XMVector4.LessOrEqual(r, zero))
{
// Total internal reflection
return(zero);
}
else
{
// R = RefractionIndex * IDotN + sqrt(R)
r = r.Sqrt();
r = XMVector.MultiplyAdd(refractionIndex, incidentDotNormal, r);
// Result = RefractionIndex * Incident - Normal * R
XMVector result = XMVector.Multiply(refractionIndex, incident);
result = XMVector.NegativeMultiplySubtract(normal, r, result);
return(result);
}
}
public static XMVector FresnelTerm(XMVector cosIncidentAngle, XMVector refractionIndex)
{
Debug.Assert(!XMVector4.IsInfinite(cosIncidentAngle), "Reviewed");
//// Result = 0.5f * (g - c)^2 / (g + c)^2 * ((c * (g + c) - 1)^2 / (c * (g - c) + 1)^2 + 1) where
//// c = CosIncidentAngle
//// g = sqrt(c^2 + RefractionIndex^2 - 1)
XMVector g = XMVector.MultiplyAdd(refractionIndex, refractionIndex, XMGlobalConstants.NegativeOne);
g = XMVector.MultiplyAdd(cosIncidentAngle, cosIncidentAngle, g);
g = g.Abs().Sqrt();
XMVector s = XMVector.Add(g, cosIncidentAngle);
XMVector d = XMVector.Subtract(g, cosIncidentAngle);
XMVector v0 = XMVector.Multiply(d, d);
XMVector v1 = XMVector.Multiply(s, s).Reciprocal();
v0 = XMVector.Multiply(XMGlobalConstants.OneHalf, v0);
v0 = XMVector.Multiply(v0, v1);
XMVector v2 = XMVector.MultiplyAdd(cosIncidentAngle, s, XMGlobalConstants.NegativeOne);
XMVector v3 = XMVector.MultiplyAdd(cosIncidentAngle, d, XMGlobalConstants.One);
v2 = XMVector.Multiply(v2, v2);
v3 = XMVector.Multiply(v3, v3);
v3 = v3.Reciprocal();
v2 = XMVector.MultiplyAdd(v2, v3, XMGlobalConstants.One);
return(XMVector.Multiply(v0, v2).Saturate());
}
public bool Intersects(BoundingSphere sh)
{
XMVector sphereCenter = sh.Center;
XMVector sphereRadius = XMVector.Replicate(sh.Radius);
XMVector boxCenter = this.center;
XMVector boxExtents = this.extents;
XMVector boxMin = boxCenter - boxExtents;
XMVector boxMax = boxCenter + boxExtents;
//// Find the distance to the nearest point on the box.
//// for each i in (x, y, z)
//// if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2
//// else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2
XMVector d = XMGlobalConstants.Zero;
// Compute d for each dimension.
XMVector lessThanMin = XMVector.Less(sphereCenter, boxMin);
XMVector greaterThanMax = XMVector.Greater(sphereCenter, boxMax);
XMVector minDelta = sphereCenter - boxMin;
XMVector maxDelta = sphereCenter - boxMax;
// Choose value for each dimension based on the comparison.
d = XMVector.Select(d, minDelta, lessThanMin);
d = XMVector.Select(d, maxDelta, greaterThanMax);
// Use a dot-product to square them and sum them together.
XMVector d2 = XMVector3.Dot(d, d);
return(XMVector3.LessOrEqual(d2, XMVector.Multiply(sphereRadius, sphereRadius)));
}
public static XMVector BaryCentricV(XMVector q0, XMVector q1, XMVector q2, XMVector f, XMVector g)
{
Debug.Assert(f.Y == f.X && f.Z == f.X && f.W == f.X, "Reviewed");
Debug.Assert(g.Y == g.X && g.Z == g.X && g.W == g.X, "Reviewed");
XMVector epsilon = XMVector.FromSplatConstant(1, 16);
XMVector s = XMVector.Add(f, g);
XMVector result;
if (XMVector4.InBounds(s, epsilon))
{
result = q0;
}
else
{
XMVector q01 = XMQuaternion.SlerpV(q0, q1, s);
XMVector q02 = XMQuaternion.SlerpV(q0, q2, s);
XMVector gs = s.Reciprocal();
gs = XMVector.Multiply(g, gs);
result = XMQuaternion.SlerpV(q01, q02, gs);
}
return(result);
}
public static void ComponentsFromNormal(out XMVector parallel, out XMVector perpendicular, XMVector v, XMVector normal)
{
XMVector scale = XMVector3.Dot(v, normal);
XMVector parallelV = XMVector.Multiply(normal, scale);
parallel = parallelV;
perpendicular = XMVector.Subtract(v, parallelV);
}
public static XMVector NormalizeEst(XMVector p)
{
//// XMPlaneNormalizeEst uses a reciprocal estimate and
//// returns QNaN on zero and infinite vectors.
XMVector result = XMVector3.ReciprocalLengthEst(p);
return(XMVector.Multiply(p, result));
}
public ContainmentType Contains(XMVector point)
{
XMVector v_center = this.center;
XMVector v_radius = XMVector.Replicate(this.radius);
XMVector distanceSquared = XMVector3.LengthSquare(point - v_center);
XMVector radiusSquared = XMVector.Multiply(v_radius, v_radius);
return(XMVector3.LessOrEqual(distanceSquared, radiusSquared) ? ContainmentType.Contains : ContainmentType.Disjoint);
}
public static XMVector NormalizeEst(XMVector v)
{
//// XMVector3NormalizeEst uses a reciprocal estimate and
//// returns QNaN on zero and infinite vectors.
XMVector result;
result = XMVector3.ReciprocalLength(v);
result = XMVector.Multiply(v, result);
return(result);
}
public static XMVector TransformNormal(XMVector v, XMMatrix m)
{
XMVector y = XMVector.SplatY(v);
XMVector x = XMVector.SplatX(v);
XMVector result = XMVector.Multiply(y, ((XMVector *)&m)[1]);
result = XMVector.MultiplyAdd(x, ((XMVector *)&m)[0], result);
return(result);
}
public static XMVector AngleBetweenVectors(XMVector v1, XMVector v2)
{
XMVector l1 = XMVector2.ReciprocalLength(v1);
XMVector l2 = XMVector2.ReciprocalLength(v2);
XMVector dot = XMVector2.Dot(v1, v2);
l1 = XMVector.Multiply(l1, l2);
return(XMVector.Multiply(dot, l1)
.Clamp(XMGlobalConstants.NegativeOne, XMGlobalConstants.One)
.ACos());
}
public static XMVector RgbToXyz(XMVector rgb)
{
XMVector scale0 = XMVector.FromFloat(0.4887180f, 0.1762044f, 0.0000000f, 0.0f);
XMVector scale1 = XMVector.FromFloat(0.3106803f, 0.8129847f, 0.0102048f, 0.0f);
XMVector scale2 = XMVector.FromFloat(0.2006017f, 0.0108109f, 0.9897952f, 0.0f);
XMVector scale = XMVector.FromFloat(1.0f / 0.17697f, 1.0f / 0.17697f, 1.0f / 0.17697f, 0.0f);
XMMatrix m = new XMMatrix(scale0, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector.Multiply(XMVector3.Transform(rgb, m), scale);
return(XMVector.Select(rgb, clr, XMGlobalConstants.Select1110));
}
public static XMVector XyzToRgb(XMVector xyz)
{
XMVector scale0 = XMVector.FromFloat(2.3706743f, -0.5138850f, 0.0052982f, 0.0f);
XMVector scale1 = XMVector.FromFloat(-0.9000405f, 1.4253036f, -0.0146949f, 0.0f);
XMVector scale2 = XMVector.FromFloat(-0.4706338f, 0.0885814f, 1.0093968f, 0.0f);
XMVector scale = XMVector.FromFloat(0.17697f, 0.17697f, 0.17697f, 0.0f);
XMMatrix m = new XMMatrix(scale0, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector3.Transform(XMVector.Multiply(xyz, scale), m);
return(XMVector.Select(xyz, clr, XMGlobalConstants.Select1110));
}
public static XMVector RotationNormal(XMVector normalAxis, float angle)
{
XMVector n = XMVector.Select(XMGlobalConstants.One, normalAxis, XMGlobalConstants.Select1110);
float sinV;
float cosV;
XMScalar.SinCos(out sinV, out cosV, 0.5f * angle);
XMVector scale = new XMVector(sinV, sinV, sinV, cosV);
return(XMVector.Multiply(n, scale));
}
public static XMVector SlerpV(XMVector q0, XMVector q1, XMVector t)
{
Debug.Assert(t.Y == t.X && t.Z == t.X && t.W == t.X, "Reviewed");
//// Result = Q0 * sin((1.0 - t) * Omega) / sin(Omega) + Q1 * sin(t * Omega) / sin(Omega)
XMVector oneMinusEpsilon = XMVector.FromFloat(1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f);
XMVector cosOmega = XMQuaternion.Dot(q0, q1);
XMVector zero = XMVector.Zero;
XMVector control = XMVector.Less(cosOmega, zero);
XMVector sign = XMVector.Select(XMGlobalConstants.One, XMGlobalConstants.NegativeOne, control);
cosOmega = XMVector.Multiply(cosOmega, sign);
control = XMVector.Less(cosOmega, oneMinusEpsilon);
XMVector sinOmega = XMVector
.NegativeMultiplySubtract(cosOmega, cosOmega, XMGlobalConstants.One)
.Sqrt();
XMVector omega = XMVector.ATan2(sinOmega, cosOmega);
XMVector signMask = XMVector.SignMask;
XMVector v01 = XMVector.ShiftLeft(t, zero, 2);
signMask = XMVector.ShiftLeft(signMask, zero, 3);
v01 = XMVector.XorInt(v01, signMask);
v01 = XMVector.Add(XMGlobalConstants.IdentityR0, v01);
XMVector invSinOmega = sinOmega.Reciprocal();
XMVector s0 = XMVector
.Multiply(v01, omega)
.Sin();
s0 = XMVector.Multiply(s0, invSinOmega);
s0 = XMVector.Select(v01, s0, control);
XMVector s1 = XMVector.SplatY(s0);
s0 = XMVector.SplatX(s0);
s1 = XMVector.Multiply(s1, sign);
XMVector result = XMVector.Multiply(q0, s0);
result = XMVector.MultiplyAdd(q1, s1, result);
return(result);
}
public static XMVector Transform(XMVector p, XMMatrix m)
{
XMVector w = XMVector.SplatW(p);
XMVector z = XMVector.SplatZ(p);
XMVector y = XMVector.SplatY(p);
XMVector x = XMVector.SplatX(p);
XMVector result = XMVector.Multiply(w, ((XMVector *)&m)[3]);
result = XMVector.MultiplyAdd(z, ((XMVector *)&m)[2], result);
result = XMVector.MultiplyAdd(y, ((XMVector *)&m)[1], result);
result = XMVector.MultiplyAdd(x, ((XMVector *)&m)[0], result);
return(result);
}
public static XMVector SquadV(XMVector q0, XMVector q1, XMVector q2, XMVector q3, XMVector t)
{
Debug.Assert(t.Y == t.X && t.Z == t.X && t.W == t.X, "Reviewed");
XMVector tp = t;
XMVector two = XMVector.FromSplatConstant(2, 0);
XMVector q03 = XMQuaternion.SlerpV(q0, q3, t);
XMVector q12 = XMQuaternion.SlerpV(q1, q2, t);
tp = XMVector.NegativeMultiplySubtract(tp, tp, tp);
tp = XMVector.Multiply(tp, two);
return(XMQuaternion.SlerpV(q03, q12, tp));
}
public static XMVector SrgbToRgb(XMVector srgb)
{
XMVector cutoff = XMVector.FromFloat(0.04045f, 0.04045f, 0.04045f, 1.0f);
XMVector invLinear = XMVector.FromFloat(1.0f / 12.92f, 1.0f / 12.92f, 1.0f / 12.92f, 1.0f);
XMVector scale = XMVector.FromFloat(1.0f / 1.055f, 1.0f / 1.055f, 1.0f / 1.055f, 1.0f);
XMVector bias = XMVector.FromFloat(0.055f, 0.055f, 0.055f, 0.0f);
XMVector gamma = XMVector.FromFloat(2.4f, 2.4f, 2.4f, 1.0f);
XMVector v = srgb.Saturate();
XMVector v0 = XMVector.Multiply(v, invLinear);
XMVector v1 = XMVector.Pow(XMVector.Multiply(XMVector.Add(v, bias), scale), gamma);
XMVector select = XMVector.Greater(v, cutoff);
v = XMVector.Select(v0, v1, select);
return(XMVector.Select(srgb, v, XMGlobalConstants.Select1110));
}
public static XMVector RgbToSrgb(XMVector rgb)
{
XMVector cutoff = XMVector.FromFloat(0.0031308f, 0.0031308f, 0.0031308f, 1.0f);
XMVector linear = XMVector.FromFloat(12.92f, 12.92f, 12.92f, 1.0f);
XMVector scale = XMVector.FromFloat(1.055f, 1.055f, 1.055f, 1.0f);
XMVector bias = XMVector.FromFloat(0.055f, 0.055f, 0.055f, 0.0f);
XMVector invGamma = XMVector.FromFloat(1.0f / 2.4f, 1.0f / 2.4f, 1.0f / 2.4f, 1.0f);
XMVector v = rgb.Saturate();
XMVector v0 = XMVector.Multiply(v, linear);
XMVector v1 = XMVector.Subtract(XMVector.Multiply(scale, XMVector.Pow(v, invGamma)), bias);
XMVector select = XMVector.Less(v, cutoff);
v = XMVector.Select(v1, v0, select);
return(XMVector.Select(rgb, v, XMGlobalConstants.Select1110));
}
public static void SquadSetup(out XMVector a, out XMVector b, out XMVector c, XMVector q0, XMVector q1, XMVector q2, XMVector q3)
{
XMVector ls12 = XMQuaternion.LengthSquare(XMVector.Add(q1, q2));
XMVector ld12 = XMQuaternion.LengthSquare(XMVector.Subtract(q1, q2));
XMVector sq2 = q2.Negate();
XMVector control1 = XMVector.Less(ls12, ld12);
sq2 = XMVector.Select(q2, sq2, control1);
XMVector ls01 = XMQuaternion.LengthSquare(XMVector.Add(q0, q1));
XMVector ld01 = XMQuaternion.LengthSquare(XMVector.Subtract(q0, q1));
XMVector sq0 = q0.Negate();
XMVector ls23 = XMQuaternion.LengthSquare(XMVector.Add(sq2, q3));
XMVector ld23 = XMQuaternion.LengthSquare(XMVector.Subtract(sq2, q3));
XMVector sq3 = q3.Negate();
XMVector control0 = XMVector.Less(ls01, ld01);
XMVector control2 = XMVector.Less(ls23, ld23);
sq0 = XMVector.Select(q0, sq0, control0);
sq3 = XMVector.Select(q3, sq3, control2);
XMVector invQ1 = XMQuaternion.Inverse(q1);
XMVector invQ2 = XMQuaternion.Inverse(sq2);
XMVector ln_q0 = XMQuaternion.Ln(XMQuaternion.Multiply(invQ1, sq0));
XMVector ln_q2 = XMQuaternion.Ln(XMQuaternion.Multiply(invQ1, sq2));
XMVector ln_q1 = XMQuaternion.Ln(XMQuaternion.Multiply(invQ2, q1));
XMVector ln_q3 = XMQuaternion.Ln(XMQuaternion.Multiply(invQ2, sq3));
XMVector negativeOneQuarter = XMVector.FromSplatConstant(-1, 2);
XMVector expQ02 = XMVector.Multiply(XMVector.Add(ln_q0, ln_q2), negativeOneQuarter);
XMVector expQ13 = XMVector.Multiply(XMVector.Add(ln_q1, ln_q3), negativeOneQuarter);
expQ02 = XMQuaternion.Exp(expQ02);
expQ13 = XMQuaternion.Exp(expQ13);
a = XMQuaternion.Multiply(q1, expQ02);
b = XMQuaternion.Multiply(sq2, expQ13);
c = sq2;
}
public static XMVector Ln(XMVector q)
{
XMVector oneMinusEpsilon = XMVector.FromFloat(1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f);
XMVector qw = XMVector.SplatW(q);
XMVector q0 = XMVector.Select(XMGlobalConstants.Select1110, q, XMGlobalConstants.Select1110);
XMVector controlW = qw.InBounds(oneMinusEpsilon);
XMVector theta = qw.ACos();
XMVector sinTheta = theta.Sin();
XMVector s = XMVector.Divide(theta, sinTheta);
XMVector result = XMVector.Multiply(q0, s);
result = XMVector.Select(q0, result, controlW);
return(result);
}
public static void IntersectPlane(out XMVector linePoint1, out XMVector linePoint2, XMVector p1, XMVector p2)
{
XMVector v1 = XMVector3.Cross(p2, p1);
XMVector lengthSq = XMVector3.LengthSquare(v1);
XMVector v2 = XMVector3.Cross(p2, v1);
XMVector p1W = XMVector.SplatW(p1);
XMVector point = XMVector.Multiply(v2, p1W);
XMVector v3 = XMVector3.Cross(v1, p1);
XMVector p2W = XMVector.SplatW(p2);
point = XMVector.MultiplyAdd(v3, p2W, point);
XMVector lineP1 = XMVector.Divide(point, lengthSq);
XMVector lineP2 = XMVector.Add(lineP1, v1);
XMVector control = XMVector.LessOrEqual(lengthSq, XMGlobalConstants.Epsilon);
linePoint1 = XMVector.Select(lineP1, XMGlobalConstants.QNaN, control);
linePoint2 = XMVector.Select(lineP2, XMGlobalConstants.QNaN, control);
}
public static XMVector Exp(XMVector q)
{
XMVector theta = XMVector3.Length(q);
XMVector sinTheta;
XMVector cosTheta;
theta.SinCos(out sinTheta, out cosTheta);
XMVector s = XMVector.Divide(sinTheta, theta);
XMVector result = XMVector.Multiply(q, s);
XMVector zero = XMVector.Zero;
XMVector control = XMVector.NearEqual(theta, zero, XMGlobalConstants.Epsilon);
result = XMVector.Select(result, q, control);
result = XMVector.Select(cosTheta, result, XMGlobalConstants.Select1110);
return(result);
}
public bool Intersects(BoundingSphere sh)
{
// Load A.
XMVector v_centerA = this.center;
XMVector v_radiusA = XMVector.Replicate(this.radius);
// Load B.
XMVector v_centerB = sh.center;
XMVector v_radiusB = XMVector.Replicate(sh.radius);
// Distance squared between centers.
XMVector delta = v_centerB - v_centerA;
XMVector distanceSquared = XMVector3.LengthSquare(delta);
// Sum of the radii squared.
XMVector radiusSquared = XMVector.Add(v_radiusA, v_radiusB);
radiusSquared = XMVector.Multiply(radiusSquared, radiusSquared);
return(XMVector3.LessOrEqual(distanceSquared, radiusSquared));
}
private static XMVector HueToClr(XMVector p, XMVector q, XMVector h)
{
XMVector oneSixth = XMVector.FromFloat(1.0f / 6.0f, 1.0f / 6.0f, 1.0f / 6.0f, 1.0f / 6.0f);
XMVector twoThirds = XMVector.FromFloat(2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f);
XMVector t = h;
if (XMVector3.Less(t, XMGlobalConstants.Zero))
{
t = XMVector.Add(t, XMGlobalConstants.One);
}
if (XMVector3.Greater(t, XMGlobalConstants.One))
{
t = XMVector.Subtract(t, XMGlobalConstants.One);
}
if (XMVector3.Less(t, oneSixth))
{
// p + (q - p) * 6 * t
XMVector t1 = XMVector.Subtract(q, p);
XMVector t2 = XMVector.Multiply(XMGlobalConstants.Six, t);
return(XMVector.MultiplyAdd(t1, t2, p));
}
if (XMVector3.Less(t, XMGlobalConstants.OneHalf))
{
return(q);
}
if (XMVector3.Less(t, twoThirds))
{
// p + (q - p) * 6 * (2/3 - t)
XMVector t1 = XMVector.Subtract(q, p);
XMVector t2 = XMVector.Multiply(XMGlobalConstants.Six, XMVector.Subtract(twoThirds, t));
return(XMVector.MultiplyAdd(t1, t2, p));
}
return(p);
}
public static XMVector ClampLengthV(XMVector v, XMVector lengthMin, XMVector lengthMax)
{
Debug.Assert(lengthMin.Y == lengthMin.X && lengthMin.Z == lengthMin.X && lengthMin.W == lengthMin.X, "Reviewed");
Debug.Assert(lengthMax.Y == lengthMax.X && lengthMax.Z == lengthMax.X && lengthMax.W == lengthMax.X, "Reviewed");
Debug.Assert(XMVector4.GreaterOrEqual(lengthMin, XMGlobalConstants.Zero), "Reviewed");
Debug.Assert(XMVector4.GreaterOrEqual(lengthMax, XMGlobalConstants.Zero), "Reviewed");
Debug.Assert(XMVector4.GreaterOrEqual(lengthMax, lengthMin), "Reviewed");
XMVector lengthSq = XMVector4.LengthSquare(v);
XMVector zero = XMVector.Zero;
XMVector reciprocalLength = lengthSq.ReciprocalSqrt();
XMVector infiniteLength = XMVector.EqualInt(lengthSq, XMGlobalConstants.Infinity);
XMVector zeroLength = XMVector.Equal(lengthSq, zero);
XMVector normal = XMVector.Multiply(v, reciprocalLength);
XMVector length = XMVector.Multiply(lengthSq, reciprocalLength);
XMVector select = XMVector.EqualInt(infiniteLength, zeroLength);
length = XMVector.Select(lengthSq, length, select);
normal = XMVector.Select(lengthSq, normal, select);
XMVector controlMax = XMVector.Greater(length, lengthMax);
XMVector controlMin = XMVector.Less(length, lengthMin);
XMVector clampLength = XMVector.Select(length, lengthMax, controlMax);
clampLength = XMVector.Select(clampLength, lengthMin, controlMin);
XMVector result = XMVector.Multiply(normal, clampLength);
// Preserve the original vector (with no precision loss) if the length falls within the given range
XMVector control = XMVector.EqualInt(controlMax, controlMin);
result = XMVector.Select(result, v, control);
return(result);
}
public ContainmentType Contains(XMVector v0, XMVector v1, XMVector v2)
{
if (!this.Intersects(v0, v1, v2))
{
return(ContainmentType.Disjoint);
}
XMVector v_center = this.center;
XMVector v_radius = XMVector.Replicate(this.radius);
XMVector radiusSquared = XMVector.Multiply(v_radius, v_radius);
XMVector distanceSquared = XMVector3.LengthSquare(v0 - v_center);
XMVector inside = XMVector.LessOrEqual(distanceSquared, radiusSquared);
distanceSquared = XMVector3.LengthSquare(v1 - v_center);
inside = XMVector.AndInt(inside, XMVector.LessOrEqual(distanceSquared, radiusSquared));
distanceSquared = XMVector3.LengthSquare(v2 - v_center);
inside = XMVector.AndInt(inside, XMVector.LessOrEqual(distanceSquared, radiusSquared));
return(XMVector3.EqualInt(inside, XMVector.TrueInt) ? ContainmentType.Contains : ContainmentType.Intersects);
}
public static XMVector XyzToSrgb(XMVector xyz)
{
XMVector scale0 = XMVector.FromFloat(3.2406f, -0.9689f, 0.0557f, 0.0f);
XMVector scale1 = XMVector.FromFloat(-1.5372f, 1.8758f, -0.2040f, 0.0f);
XMVector scale2 = XMVector.FromFloat(-0.4986f, 0.0415f, 1.0570f, 0.0f);
XMVector cutoff = XMVector.FromFloat(0.0031308f, 0.0031308f, 0.0031308f, 0.0f);
XMVector exp = XMVector.FromFloat(1.0f / 2.4f, 1.0f / 2.4f, 1.0f / 2.4f, 1.0f);
XMMatrix m = new XMMatrix(scale0, scale1, scale2, XMGlobalConstants.Zero);
XMVector lclr = XMVector3.Transform(xyz, m);
XMVector sel = XMVector.Greater(lclr, cutoff);
// clr = 12.92 * lclr for lclr <= 0.0031308f
XMVector smallC = XMVector.Multiply(lclr, XMGlobalConstants.MsrgbScale);
// clr = (1+a)*pow(lclr, 1/2.4) - a for lclr > 0.0031308 (where a = 0.055)
XMVector largeC = XMVector.Subtract(XMVector.Multiply(XMGlobalConstants.MsrgbA1, XMVector.Pow(lclr, exp)), XMGlobalConstants.MsrgbA);
XMVector clr = XMVector.Select(smallC, largeC, sel);
return(XMVector.Select(xyz, clr, XMGlobalConstants.Select1110));
}
public static XMVector HslToRgb(XMVector hsl)
{
XMVector oneThird = XMVector.FromFloat(1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f);
XMVector s = XMVector.SplatY(hsl);
XMVector l = XMVector.SplatZ(hsl);
if (XMVector3.NearEqual(s, XMGlobalConstants.Zero, XMGlobalConstants.Epsilon))
{
// Achromatic
return(XMVector.Select(hsl, l, XMGlobalConstants.Select1110));
}
else
{
XMVector h = XMVector.SplatX(hsl);
XMVector q;
if (XMVector3.Less(l, XMGlobalConstants.OneHalf))
{
q = XMVector.Multiply(l, XMVector.Add(XMGlobalConstants.One, s));
}
else
{
q = XMVector.Subtract(XMVector.Add(l, s), XMVector.Multiply(l, s));
}
XMVector p = XMVector.Subtract(XMVector.Multiply(XMGlobalConstants.Two, l), q);
XMVector r = XMColor.HueToClr(p, q, XMVector.Add(h, oneThird));
XMVector g = XMColor.HueToClr(p, q, h);
XMVector b = XMColor.HueToClr(p, q, XMVector.Subtract(h, oneThird));
XMVector rg = XMVector.Select(g, r, XMGlobalConstants.Select1000);
XMVector ba = XMVector.Select(hsl, b, XMGlobalConstants.Select1110);
return(XMVector.Select(ba, rg, XMGlobalConstants.Select1100));
}
}
public static XMVector IntersectLine(XMVector line1Point1, XMVector line1Point2, XMVector line2Point1, XMVector line2Point2)
{
XMVector v1 = XMVector.Subtract(line1Point2, line1Point1);
XMVector v2 = XMVector.Subtract(line2Point2, line2Point1);
XMVector v3 = XMVector.Subtract(line1Point1, line2Point1);
XMVector c1 = XMVector2.Cross(v1, v2);
XMVector c2 = XMVector2.Cross(v2, v3);
XMVector result;
XMVector zero = XMVector.Zero;
if (XMVector2.NearEqual(c1, zero, XMGlobalConstants.Epsilon))
{
if (XMVector2.NearEqual(c2, zero, XMGlobalConstants.Epsilon))
{
// Coincident
result = XMGlobalConstants.Infinity;
}
else
{
// Parallel
result = XMGlobalConstants.QNaN;
}
}
else
{
//// Intersection point = Line1Point1 + V1 * (C2 / C1)
XMVector scale = c1.Reciprocal();
scale = XMVector.Multiply(c2, scale);
result = XMVector.MultiplyAdd(v1, scale, line1Point1);
}
return(result);
}