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 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 static XMVector RgbToHsv(XMVector rgb)
{
XMVector r = XMVector.SplatX(rgb);
XMVector g = XMVector.SplatY(rgb);
XMVector b = XMVector.SplatZ(rgb);
XMVector min = XMVector.Min(r, XMVector.Min(g, b));
XMVector v = XMVector.Max(r, XMVector.Max(g, b));
XMVector d = XMVector.Subtract(v, min);
XMVector s = XMVector3.NearEqual(v, XMGlobalConstants.Zero, XMGlobalConstants.Epsilon) ?
XMGlobalConstants.Zero :
XMVector.Divide(d, v);
if (XMVector3.Less(d, XMGlobalConstants.Epsilon))
{
// Achromatic, assume H of 0
XMVector hv = XMVector.Select(v, XMGlobalConstants.Zero, XMGlobalConstants.Select1000);
XMVector hva = XMVector.Select(rgb, hv, XMGlobalConstants.Select1110);
return(XMVector.Select(s, hva, XMGlobalConstants.Select1011));
}
else
{
XMVector h;
if (XMVector3.Equal(r, v))
{
// Red is max
h = XMVector.Divide(XMVector.Subtract(g, b), d);
if (XMVector3.Less(g, b))
{
h = XMVector.Add(h, XMGlobalConstants.Six);
}
}
else if (XMVector3.Equal(g, v))
{
// Green is max
h = XMVector.Divide(XMVector.Subtract(b, r), d);
h = XMVector.Add(h, XMGlobalConstants.Two);
}
else
{
// Blue is max
h = XMVector.Divide(XMVector.Subtract(r, g), d);
h = XMVector.Add(h, XMGlobalConstants.Four);
}
h = XMVector.Divide(h, XMGlobalConstants.Six);
XMVector hv = XMVector.Select(v, h, XMGlobalConstants.Select1000);
XMVector hva = XMVector.Select(rgb, hv, XMGlobalConstants.Select1110);
return(XMVector.Select(s, hva, XMGlobalConstants.Select1011));
}
}
public static XMVector Reflect(XMVector incident, XMVector normal)
{
//// Result = Incident - (2 * dot(Incident, Normal)) * Normal
XMVector result = XMVector4.Dot(incident, normal);
result = XMVector.Add(result, result);
result = XMVector.NegativeMultiplySubtract(result, normal, incident);
return(result);
}
public static BoundingBox CreateFromSphere(BoundingSphere sh)
{
XMVector sp_Center = sh.Center;
XMVector sh_Radius = XMVector.Replicate(sh.Radius);
XMVector min = XMVector.Subtract(sp_Center, sh_Radius);
XMVector max = XMVector.Add(sp_Center, sh_Radius);
Debug.Assert(XMVector3.LessOrEqual(min, max), "Reviewed");
return(new BoundingBox((min + max) * 0.5f, (max - min) * 0.5f));
}
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 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 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 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 BoundingBox CreateMerged(BoundingBox b1, BoundingBox b2)
{
XMVector b1_Center = b1.center;
XMVector b1_Extents = b1.extents;
XMVector b2_Center = b2.center;
XMVector b2_Extents = b2.extents;
XMVector min = XMVector.Subtract(b1_Center, b1_Extents);
min = XMVector.Min(min, XMVector.Subtract(b2_Center, b2_Extents));
XMVector max = XMVector.Add(b1_Center, b1_Extents);
max = XMVector.Max(max, XMVector.Add(b2_Center, b2_Extents));
Debug.Assert(XMVector3.LessOrEqual(min, max), "Reviewed");
return(new BoundingBox((min + max) * 0.5f, (max - min) * 0.5f));
}
public static XMVector Orthogonal(XMVector v)
{
XMVector zero = XMVector.Zero;
XMVector z = XMVector.SplatZ(v);
XMVector yzyy = new XMVector(v.Y, v.Z, v.Y, v.Y);
XMVector negativeV = XMVector.Subtract(zero, v);
XMVector z_isNegative = XMVector.Less(z, zero);
XMVector yzyyIsNegative = XMVector.Less(yzyy, zero);
XMVector s = XMVector.Add(yzyy, z);
XMVector d = XMVector.Subtract(yzyy, z);
XMVector select = XMVector.EqualInt(z_isNegative, yzyyIsNegative);
XMVector r0 = new XMVector(s.X, negativeV.X, negativeV.X, negativeV.X);
XMVector r1 = new XMVector(d.X, v.X, v.X, v.X);
return(XMVector.Select(r1, r0, select));
}
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 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 SrgbToXyz(XMVector srgb)
{
XMVector scale0 = XMVector.FromFloat(0.4124f, 0.2126f, 0.0193f, 0.0f);
XMVector scale1 = XMVector.FromFloat(0.3576f, 0.7152f, 0.1192f, 0.0f);
XMVector scale2 = XMVector.FromFloat(0.1805f, 0.0722f, 0.9505f, 0.0f);
XMVector cutoff = XMVector.FromFloat(0.04045f, 0.04045f, 0.04045f, 0.0f);
XMVector exp = XMVector.FromFloat(2.4f, 2.4f, 2.4f, 1.0f);
XMVector sel = XMVector.Greater(srgb, cutoff);
// lclr = clr / 12.92
XMVector smallC = XMVector.Divide(srgb, XMGlobalConstants.MsrgbScale);
// lclr = pow( (clr + a) / (1+a), 2.4 )
XMVector largeC = XMVector.Pow(XMVector.Divide(XMVector.Add(srgb, XMGlobalConstants.MsrgbA), XMGlobalConstants.MsrgbA1), exp);
XMVector lclr = XMVector.Select(smallC, largeC, sel);
XMMatrix m = new XMMatrix(scale0, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector3.Transform(lclr, m);
return(XMVector.Select(srgb, clr, XMGlobalConstants.Select1110));
}
public static BoundingSphere CreateMerged(BoundingSphere s1, BoundingSphere s2)
{
XMVector center1 = s1.center;
float r1 = s1.radius;
XMVector center2 = s2.center;
float r2 = s2.radius;
XMVector v = XMVector.Subtract(center2, center1);
XMVector dist = XMVector3.Length(v);
float d = dist.X;
if (r1 + r2 >= d)
{
if (r1 - r2 >= d)
{
return(s1);
}
else if (r2 - r1 >= d)
{
return(s2);
}
}
XMVector n = XMVector.Divide(v, dist);
float t1 = Math.Min(-r1, d - r2);
float t2 = Math.Max(r1, d + r2);
float t_5 = (t2 - t1) * 0.5f;
XMVector n_center = XMVector.Add(center1, XMVector.Multiply(n, XMVector.Replicate(t_5 + t1)));
return(new BoundingSphere(n_center, t_5));
}
public static XMVector RgbToHsl(XMVector rgb)
{
XMVector r = XMVector.SplatX(rgb);
XMVector g = XMVector.SplatY(rgb);
XMVector b = XMVector.SplatZ(rgb);
XMVector min = XMVector.Min(r, XMVector.Min(g, b));
XMVector max = XMVector.Max(r, XMVector.Max(g, b));
XMVector l = XMVector.Multiply(XMVector.Add(min, max), XMGlobalConstants.OneHalf);
XMVector d = XMVector.Subtract(max, min);
XMVector la = XMVector.Select(rgb, l, XMGlobalConstants.Select1110);
if (XMVector3.Less(d, XMGlobalConstants.Epsilon))
{
// Achromatic, assume H and S of 0
return(XMVector.Select(la, XMGlobalConstants.Zero, XMGlobalConstants.Select1100));
}
else
{
XMVector s;
XMVector h;
XMVector d2 = XMVector.Add(min, max);
if (XMVector3.Greater(l, XMGlobalConstants.OneHalf))
{
// d / (2-max-min)
s = XMVector.Divide(d, XMVector.Subtract(XMGlobalConstants.Two, d2));
}
else
{
// d / (max+min)
s = XMVector.Divide(d, d2);
}
if (XMVector3.Equal(r, max))
{
// Red is max
h = XMVector.Divide(XMVector.Subtract(g, b), d);
}
else if (XMVector3.Equal(g, max))
{
// Green is max
h = XMVector.Divide(XMVector.Subtract(b, r), d);
h = XMVector.Add(h, XMGlobalConstants.Two);
}
else
{
// Blue is max
h = XMVector.Divide(XMVector.Subtract(r, g), d);
h = XMVector.Add(h, XMGlobalConstants.Four);
}
h = XMVector.Divide(h, XMGlobalConstants.Six);
if (XMVector3.Less(h, XMGlobalConstants.Zero))
{
h = XMVector.Add(h, XMGlobalConstants.One);
}
XMVector lha = XMVector.Select(la, h, XMGlobalConstants.Select1100);
return(XMVector.Select(s, lha, XMGlobalConstants.Select1011));
}
}