public static XMVector Unproject(
XMVector v,
float viewportX,
float viewportY,
float viewportWidth,
float viewportHeight,
float viewportMinZ,
float viewportMaxZ,
XMMatrix projection,
XMMatrix view,
XMMatrix world)
{
XMVector d = XMVector.FromFloat(-1.0f, 1.0f, 0.0f, 0.0f);
XMVector scale = new XMVector(viewportWidth * 0.5f, -viewportHeight * 0.5f, viewportMaxZ - viewportMinZ, 1.0f);
scale = scale.Reciprocal();
XMVector offset = new XMVector(-viewportX, -viewportY, -viewportMinZ, 0.0f);
offset = XMVector.MultiplyAdd(scale, offset, d);
XMMatrix transform = XMMatrix.Multiply(world, view);
transform = XMMatrix.Multiply(transform, projection);
transform = transform.Inverse();
XMVector result = XMVector.MultiplyAdd(v, scale, offset);
return(XMVector3.TransformCoord(result, transform));
}
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 incidentDotNornal = XMVector3.Dot(incident, normal);
// R = 1.0f - RefractionIndex * RefractionIndex * (1.0f - IDotN * IDotN)
XMVector r = XMVector.NegativeMultiplySubtract(incidentDotNornal, incidentDotNornal, XMGlobalConstants.One);
r = XMVector.Multiply(r, refractionIndex);
r = XMVector.NegativeMultiplySubtract(r, refractionIndex, XMGlobalConstants.One);
if (r.X <= zero.X && r.Y <= zero.Y && r.Z <= zero.Z && r.W <= zero.W)
{
// Total internal reflection
return(zero);
}
else
{
// R = RefractionIndex * IDotN + sqrt(R)
r = r.Sqrt();
r = XMVector.MultiplyAdd(refractionIndex, incidentDotNornal, r);
// Result = RefractionIndex * Incident - Normal * R
XMVector result = XMVector.Multiply(refractionIndex, incident);
result = XMVector.NegativeMultiplySubtract(normal, r, result);
return(result);
}
}
public static XMVector Project(
XMVector v,
float viewportX,
float viewportY,
float viewportWidth,
float viewportHeight,
float viewportMinZ,
float viewportMaxZ,
XMMatrix projection,
XMMatrix view,
XMMatrix world)
{
float halfViewportWidth = viewportWidth * 0.5f;
float halfViewportHeight = viewportHeight * 0.5f;
XMVector scale = new XMVector(halfViewportWidth, -halfViewportHeight, viewportMaxZ - viewportMinZ, 0.0f);
XMVector offset = new XMVector(viewportX + halfViewportWidth, viewportY + halfViewportHeight, viewportMinZ, 0.0f);
XMMatrix transform = XMMatrix.Multiply(world, view);
transform = XMMatrix.Multiply(transform, projection);
XMVector result = XMVector3.TransformCoord(v, transform);
result = XMVector.MultiplyAdd(result, scale, offset);
return(result);
}
public static XMVector AngleBetweenNormals(XMVector n1, XMVector n2)
{
return(XMVector3
.Dot(n1, n2)
.Clamp(XMGlobalConstants.NegativeOne, XMGlobalConstants.One)
.ACos());
}
public static XMVector ClampLength(XMVector v, float lengthMin, float lengthMax)
{
XMVector clampMax = XMVector.Replicate(lengthMax);
XMVector clampMin = XMVector.Replicate(lengthMin);
return(XMVector3.ClampLengthV(v, clampMin, clampMax));
}
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 FromPointNormal(XMVector point, XMVector normal)
{
XMVector w = XMVector3
.Dot(point, normal)
.Negate();
return(XMVector.Select(w, normal, XMGlobalConstants.Select1110));
}
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 static XMVector RotationAxis(XMVector axis, float angle)
{
Debug.Assert(!XMVector3.Equal(axis, XMGlobalConstants.Zero), "Reviewed");
Debug.Assert(!XMVector3.IsInfinite(axis), "Reviewed");
XMVector normal = XMVector3.Normalize(axis);
return(XMQuaternion.RotationNormal(normal, angle));
}
public static XMVector YuvToRgb(XMVector yuv)
{
XMVector scale1 = XMVector.FromFloat(0.0f, -0.395f, 2.032f, 0.0f);
XMVector scale2 = XMVector.FromFloat(1.140f, -0.581f, 0.0f, 0.0f);
XMMatrix m = new XMMatrix(XMGlobalConstants.One, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector3.Transform(yuv, m);
return(XMVector.Select(yuv, clr, XMGlobalConstants.Select1110));
}
public static XMVector YuvToRgbHD(XMVector yuv)
{
XMVector scale1 = XMVector.FromFloat(0.0f, -0.2153f, 2.1324f, 0.0f);
XMVector scale2 = XMVector.FromFloat(1.2803f, -0.3806f, 0.0f, 0.0f);
XMMatrix m = new XMMatrix(XMGlobalConstants.One, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector3.Transform(yuv, m);
return(XMVector.Select(yuv, clr, XMGlobalConstants.Select1110));
}
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 = XMVector3.Dot(incident, normal);
result = XMVector.Add(result, result);
result = XMVector.NegativeMultiplySubtract(result, normal, incident);
return(result);
}
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 RgbToYuvHD(XMVector rgb)
{
XMVector scale0 = XMVector.FromFloat(0.2126f, -0.0997f, 0.6150f, 0.0f);
XMVector scale1 = XMVector.FromFloat(0.7152f, -0.3354f, -0.5586f, 0.0f);
XMVector scale2 = XMVector.FromFloat(0.0722f, 0.4351f, -0.0564f, 0.0f);
XMMatrix m = new XMMatrix(scale0, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector3.Transform(rgb, m);
return(XMVector.Select(rgb, clr, XMGlobalConstants.Select1110));
}
public static XMVector RgbToYuv(XMVector rgb)
{
XMVector scale0 = XMVector.FromFloat(0.299f, -0.147f, 0.615f, 0.0f);
XMVector scale1 = XMVector.FromFloat(0.587f, -0.289f, -0.515f, 0.0f);
XMVector scale2 = XMVector.FromFloat(0.114f, 0.436f, -0.100f, 0.0f);
XMMatrix m = new XMMatrix(scale0, scale1, scale2, XMGlobalConstants.Zero);
XMVector clr = XMVector3.Transform(rgb, m);
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 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 AngleBetweenVectors(XMVector v1, XMVector v2)
{
XMVector l1 = XMVector3.ReciprocalLength(v1);
XMVector l2 = XMVector3.ReciprocalLength(v2);
XMVector dot = XMVector3.Dot(v1, v2);
l1 = XMVector.Multiply(l1, l2);
return(XMVector
.Multiply(dot, l1)
.Clamp(XMGlobalConstants.NegativeOne, XMGlobalConstants.One)
.ACos());
}
public static XMVector FromPoints(XMVector point1, XMVector point2, XMVector point3)
{
XMVector v21 = XMVector.Subtract(point1, point2);
XMVector v31 = XMVector.Subtract(point1, point3);
XMVector n = XMVector3.Cross(v21, v31);
n = XMVector3.Normalize(n);
XMVector d = XMPlane
.DotNormal(n, point1)
.Negate();
return(XMVector.Select(d, n, XMGlobalConstants.Select1110));
}
public static XMVector Normalize(XMVector v)
{
XMVector result = XMVector3.Length(v);
float length = result.X;
// Prevent divide by zero
if (length > 0)
{
length = 1.0f / length;
}
return(new XMVector(
v.X * length,
v.Y * length,
v.Z * length,
v.W * length));
}
public static XMVector IntersectLine(XMVector p, XMVector linePoint1, XMVector linePoint2)
{
XMVector v1 = XMVector3.Dot(p, linePoint1);
XMVector v2 = XMVector3.Dot(p, linePoint2);
XMVector d = XMVector.Subtract(v1, v2);
XMVector vt = XMPlane.DotCoord(p, linePoint1);
vt = XMVector.Divide(vt, d);
XMVector point = XMVector.Subtract(linePoint2, linePoint1);
point = XMVector.MultiplyAdd(point, vt, linePoint1);
XMVector control = XMVector.NearEqual(d, XMGlobalConstants.Zero, XMGlobalConstants.Epsilon);
return(XMVector.Select(point, XMGlobalConstants.QNaN, control));
}
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);
}
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, "Reviewed");
Debug.Assert(lengthMax.Y == lengthMax.X && lengthMax.Z == lengthMax.X, "Reviewed");
Debug.Assert(XMVector3.GreaterOrEqual(lengthMin, XMGlobalConstants.Zero), "Reviewed");
Debug.Assert(XMVector3.GreaterOrEqual(lengthMax, XMGlobalConstants.Zero), "Reviewed");
Debug.Assert(XMVector3.GreaterOrEqual(lengthMax, lengthMin), "Reviewed");
XMVector lengthSq = XMVector3.LengthSquare(v);
XMVector zero = XMVector.Zero;
XMVector reciprocalLength = lengthSq.ReciprocalSqrt();
XMVector infiniteLength = XMVector.EqualInt(lengthSq, XMGlobalConstants.Infinity);
XMVector zeroLength = XMVector.EqualInt(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 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 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 XMVector LinePointDistance(XMVector linePoint1, XMVector linePoint2, XMVector point)
{
//// Given a vector PointVector from LinePoint1 to Point and a vector
//// LineVector from LinePoint1 to LinePoint2, the scaled distance
//// PointProjectionScale from LinePoint1 to the perpendicular projection
//// of PointVector onto the line is defined as:
////
//// PointProjectionScale = dot(PointVector, LineVector) / LengthSq(LineVector)
XMVector pointVector = XMVector.Subtract(point, linePoint1);
XMVector lineVector = XMVector.Subtract(linePoint2, linePoint1);
XMVector lengthSq = XMVector3.LengthSquare(lineVector);
XMVector pointProjectionScale = XMVector3.Dot(pointVector, lineVector);
pointProjectionScale = XMVector.Divide(pointProjectionScale, lengthSq);
XMVector distanceVector = XMVector.Multiply(lineVector, pointProjectionScale);
distanceVector = XMVector.Subtract(pointVector, distanceVector);
return(XMVector3.Length(distanceVector));
}