//-----------------------------------------------------------------------------------------------
float Compute2dFractalNoise( float posX, float posY, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float invScale = (1.f / scale);
Vector2 currentPos( posX * invScale, posY * invScale );
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine noise values at nearby integer "grid point" positions
Vector2 cellMins( FastFloor( currentPos.x ), FastFloor( currentPos.y ) );
int indexWestX = (int) cellMins.x;
int indexSouthY = (int) cellMins.y;
int indexEastX = indexWestX + 1;
int indexNorthY = indexSouthY + 1;
float valueSouthWest = Get2dNoiseZeroToOne( indexWestX, indexSouthY, seed );
float valueSouthEast = Get2dNoiseZeroToOne( indexEastX, indexSouthY, seed );
float valueNorthWest = Get2dNoiseZeroToOne( indexWestX, indexNorthY, seed );
float valueNorthEast = Get2dNoiseZeroToOne( indexEastX, indexNorthY, seed );
// Do a smoothed (nonlinear) weighted average of nearby grid point values
Vector2 displacementFromMins = currentPos - cellMins;
float weightEast = SmoothStep( displacementFromMins.x );
float weightNorth = SmoothStep( displacementFromMins.y );
float weightWest = 1.f - weightEast;
float weightSouth = 1.f - weightNorth;
float blendSouth = (weightEast * valueSouthEast) + (weightWest * valueSouthWest);
float blendNorth = (weightEast * valueNorthEast) + (weightWest * valueNorthWest);
float blendTotal = (weightSouth * blendSouth) + (weightNorth * blendNorth);
float noiseThisOctave = 2.f * (blendTotal - 0.5f); // Map from [0,1] to [-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPos *= octaveScale;
currentPos.x += OCTAVE_OFFSET; // Add "irrational" offsets to noise position components
currentPos.y += OCTAVE_OFFSET; // at each octave to break up their grid alignment
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
//-----------------------------------------------------------------------------------------------
// Perlin noise is fractal noise with "gradient vector smoothing" applied.
//
// In 1D, the gradients are trivial: -1.0 or 1.0, so resulting noise is boring at one octave.
//
float Compute1dPerlinNoise( float position, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
const float gradients[2] = { -1.f, 1.f }; // 1D unit "gradient" vectors; one back, one forward
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float currentPosition = position * (1.f / scale);
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine random "gradient vectors" (just +1 or -1 for 1D Perlin) for surrounding corners
float positionFloor = (float) FastFloor( currentPosition );
int indexWest = (int) positionFloor;
int indexEast = indexWest + 1;
float gradientWest = gradients[ Get1dNoiseUint( indexWest, seed ) & 0x00000001 ];
float gradientEast = gradients[ Get1dNoiseUint( indexEast, seed ) & 0x00000001 ];
// Dot each point's gradient with displacement from point to position
float displacementFromWest = currentPosition - positionFloor; // always positive
float displacementFromEast = displacementFromWest - 1.f; // always negative
float dotWest = gradientWest * displacementFromWest; // 1D "dot product" is... multiply
float dotEast = gradientEast * displacementFromEast;
// Do a smoothed (nonlinear) weighted average of dot results
float weightEast = SmoothStep( displacementFromWest );
float weightWest = 1.f - weightEast;
float blendTotal = (weightWest * dotWest) + (weightEast * dotEast);
float noiseThisOctave = 2.f * blendTotal; // 1D Perlin is in [-.5,.5]; map to [-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPosition *= octaveScale;
currentPosition += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
//-----------------------------------------------------------------------------------------------
float Compute1dFractalNoise( float position, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float currentPosition = position * (1.f / scale);
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine noise values at nearby integer "grid point" positions
float positionFloor = FastFloor( currentPosition );
int indexWest = (int) positionFloor;
int indexEast = indexWest + 1;
float valueWest = Get1dNoiseZeroToOne( indexWest, seed );
float valueEast = Get1dNoiseZeroToOne( indexEast, seed );
// Do a smoothed (nonlinear) weighted average of nearby grid point values
float distanceFromWest = currentPosition - positionFloor;
float weightEast = SmoothStep( distanceFromWest ); // Gives rounder (nonlinear) results
float weightWest = 1.f - weightEast;
float noiseZeroToOne = (valueWest * weightWest) + (valueEast * weightEast);
float noiseThisOctave = 2.f * (noiseZeroToOne - 0.5f); // Map from [0,1] to [-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPosition *= octaveScale;
currentPosition += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used!
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
/// <summary>
/// 2D simplex noise
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
public static float Generate(float x, float y)
{
const float F2 = 0.366025403f; // F2 = 0.5*(sqrt(3.0)-1.0)
const float G2 = 0.211324865f; // G2 = (3.0-Math.sqrt(3.0))/6.0
float n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
float s = (x+y)*F2; // Hairy factor for 2D
float xs = x + s;
float ys = y + s;
int i = FastFloor(xs);
int j = FastFloor(ys);
float t = (float)(i+j)*G2;
float X0 = i-t; // Unskew the cell origin back to (x,y) space
float Y0 = j-t;
float x0 = x-X0; // The x,y distances from the cell origin
float y0 = y-Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
float y2 = y0 - 1.0f + 2.0f * G2;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i % 256;
int jj = j % 256;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0*x0-y0*y0;
if(t0 < 0.0f) n0 = 0.0f;
else {
t0 *= t0;
n0 = t0 * t0 * grad(perm[ii+perm[jj]], x0, y0);
}
float t1 = 0.5f - x1*x1-y1*y1;
if(t1 < 0.0f) n1 = 0.0f;
else {
t1 *= t1;
n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1]], x1, y1);
}
float t2 = 0.5f - x2*x2-y2*y2;
if(t2 < 0.0f) n2 = 0.0f;
else {
t2 *= t2;
n2 = t2 * t2 * grad(perm[ii+1+perm[jj+1]], x2, y2);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].
return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
}
float SimplexNoise::Raw_Sample_2D(float x, float y)
{
// Noise contributions from the three corners
float n0, n1, n2;
// Skew the input space to determine which simplex cell we're in
float F2 = 0.5f * (sqrtf(3.0f) - 1.0f);
// Hairy factor for 2D
float s = (x + y) * F2;
int i = FastFloor( x + s );
int j = FastFloor( y + s );
float G2 = (3.0f - sqrtf(3.0f)) / 6.0f;
float t = (i + j) * G2;
// Unskew the cell origin back to (x,y) space
float X0 = i-t;
float Y0 = j-t;
// The x,y distances from the cell origin
float x0 = x-X0;
float y0 = y-Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
// lower triangle, XY order: (0,0)->(1,0)->(1,1)
if (x0 > y0)
{
i1=1;
j1=0;
}
// upper triangle, YX order: (0,0)->(0,1)->(1,1)
else
{
i1=0;
j1=1;
}
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
float y2 = y0 - 1.0f + 2.0f * G2;
// Work out the hashed gradient indices of the three simplex corners
int ii = i & 255;
int jj = j & 255;
int gi0 = m_permutations[ii+m_permutations[jj]] % 12;
int gi1 = m_permutations[ii+i1+m_permutations[jj+j1]] % 12;
int gi2 = m_permutations[ii+1+m_permutations[jj+1]] % 12;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0*x0-y0*y0;
if (t0 < 0)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * Dot(m_gradiant3D[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
}
float t1 = 0.5f - x1*x1-y1*y1;
if (t1 < 0)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * Dot(m_gradiant3D[gi1], x1, y1);
}
float t2 = 0.5f - x2*x2-y2*y2;
if (t2 < 0)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * Dot(m_gradiant3D[gi2], x2, y2);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].
return 70.0f * (n0 + n1 + n2);
}
float SimplexNoise::Raw_Sample_4D(float x, float y, float z, float w)
{
// The skewing and unskewing factors are hairy again for the 4D case
float F4 = (sqrtf(5.0f)-1.0f)/4.0f;
float G4 = (5.0f-sqrtf(5.0f))/20.0f;
float n0, n1, n2, n3, n4; // Noise contributions from the five corners
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
float s = (x + y + z + w) * F4; // Factor for 4D skewing
int i = FastFloor(x + s);
int j = FastFloor(y + s);
int k = FastFloor(z + s);
int l = FastFloor(w + s);
float t = (i + j + k + l) * G4; // Factor for 4D unskewing
float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
float Y0 = j - t;
float Z0 = k - t;
float W0 = l - t;
float x0 = x - X0; // The x,y,z,w distances from the cell origin
float y0 = y - Y0;
float z0 = z - Z0;
float w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// The method below is a good way of finding the ordering of x,y,z,w and
// then find the correct traversal order for the simplex we're in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to add up binary bits
// for an integer index.
int c1 = (x0 > y0) ? 32 : 0;
int c2 = (x0 > z0) ? 16 : 0;
int c3 = (y0 > z0) ? 8 : 0;
int c4 = (x0 > w0) ? 4 : 0;
int c5 = (y0 > w0) ? 2 : 0;
int c6 = (z0 > w0) ? 1 : 0;
int c = c1 + c2 + c3 + c4 + c5 + c6;
int i1, j1, k1, l1; // The integer offsets for the second simplex corner
int i2, j2, k2, l2; // The integer offsets for the third simplex corner
int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = m_simplex[c][0]>=3 ? 1 : 0;
j1 = m_simplex[c][1]>=3 ? 1 : 0;
k1 = m_simplex[c][2]>=3 ? 1 : 0;
l1 = m_simplex[c][3]>=3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = m_simplex[c][0]>=2 ? 1 : 0;
j2 = m_simplex[c][1]>=2 ? 1 : 0;
k2 = m_simplex[c][2]>=2 ? 1 : 0;
l2 = m_simplex[c][3]>=2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = m_simplex[c][0]>=1 ? 1 : 0;
j3 = m_simplex[c][1]>=1 ? 1 : 0;
k3 = m_simplex[c][2]>=1 ? 1 : 0;
l3 = m_simplex[c][3]>=1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
float y1 = y0 - j1 + G4;
float z1 = z0 - k1 + G4;
float w1 = w0 - l1 + G4;
float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords
float y2 = y0 - j2 + 2.0f*G4;
float z2 = z0 - k2 + 2.0f*G4;
float w2 = w0 - l2 + 2.0f*G4;
float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords
float y3 = y0 - j3 + 3.0f*G4;
float z3 = z0 - k3 + 3.0f*G4;
float w3 = w0 - l3 + 3.0f*G4;
float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords
float y4 = y0 - 1.0f + 4.0f*G4;
float z4 = z0 - 1.0f + 4.0f*G4;
float w4 = w0 - 1.0f + 4.0f*G4;
// Work out the hashed gradient indices of the five simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int ll = l & 255;
int gi0 = m_permutations[ii+m_permutations[jj+m_permutations[kk+m_permutations[ll]]]] % 32;
int gi1 = m_permutations[ii+i1+m_permutations[jj+j1+m_permutations[kk+k1+m_permutations[ll+l1]]]] % 32;
int gi2 = m_permutations[ii+i2+m_permutations[jj+j2+m_permutations[kk+k2+m_permutations[ll+l2]]]] % 32;
int gi3 = m_permutations[ii+i3+m_permutations[jj+j3+m_permutations[kk+k3+m_permutations[ll+l3]]]] % 32;
int gi4 = m_permutations[ii+1+m_permutations[jj+1+m_permutations[kk+1+m_permutations[ll+1]]]] % 32;
// Calculate the contribution from the five corners
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if (t0 < 0)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * Dot(m_gradiant4D[gi0], x0, y0, z0, w0);
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if(t1 < 0)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * Dot(m_gradiant4D[gi1], x1, y1, z1, w1);
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if (t2 < 0)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * Dot(m_gradiant4D[gi2], x2, y2, z2, w2);
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if (t3 < 0)
{
n3 = 0.0f;
}
else
{
t3 *= t3;
n3 = t3 * t3 * Dot(m_gradiant4D[gi3], x3, y3, z3, w3);
}
float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if (t4 < 0)
{
n4 = 0.0f;
}
else
{
t4 *= t4;
n4 = t4 * t4 * Dot(m_gradiant4D[gi4], x4, y4, z4, w4);
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0f * (n0 + n1 + n2 + n3 + n4);
}
float SimplexNoise::Raw_Sample_3D(float x, float y, float z)
{
float n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
float F3 = 1.0f/3.0f;
float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
int i = FastFloor(x+s);
int j = FastFloor(y+s);
int k = FastFloor(z+s);
float G3 = 1.0f/6.0f; // Very nice and simple unskew factor, too
float t = (i+j+k)*G3;
float X0 = i-t; // Unskew the cell origin back to (x,y,z) space
float Y0 = j-t;
float Z0 = k-t;
float x0 = x-X0; // The x,y,z distances from the cell origin
float y0 = y-Y0;
float z0 = z-Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
if (x0 >= y0)
{
// X Y Z order
if (y0 >= z0)
{
i1=1;
j1=0;
k1=0;
i2=1;
j2=1;
k2=0;
}
// X Z Y order
else if (x0 >= z0)
{
i1=1;
j1=0;
k1=0;
i2=1;
j2=0;
k2=1;
}
// Z X Y order
else
{
i1=0;
j1=0;
k1=1;
i2=1;
j2=0;
k2=1;
}
}
// x0<y0
else
{
// Z Y X order
if (y0 < z0)
{
i1=0;
j1=0;
k1=1;
i2=0;
j2=1;
k2=1;
}
// Y Z X order
else if (x0 < z0)
{
i1=0;
j1=1;
k1=0;
i2=0;
j2=1;
k2=1;
}
// Y X Z order
else
{
i1=0;
j1=1;
k1=0;
i2=1;
j2=1;
k2=0;
}
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords
float y2 = y0 - j2 + 2.0f*G3;
float z2 = z0 - k2 + 2.0f*G3;
float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords
float y3 = y0 - 1.0f + 3.0f*G3;
float z3 = z0 - 1.0f + 3.0f*G3;
// Work out the hashed gradient indices of the four simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int gi0 = m_permutations[ii+m_permutations[jj+m_permutations[kk]]] % 12;
int gi1 = m_permutations[ii+i1+m_permutations[jj+j1+m_permutations[kk+k1]]] % 12;
int gi2 = m_permutations[ii+i2+m_permutations[jj+j2+m_permutations[kk+k2]]] % 12;
int gi3 = m_permutations[ii+1+m_permutations[jj+1+m_permutations[kk+1]]] % 12;
// Calculate the contribution from the four corners
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
if (t0 < 0)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * Dot(m_gradiant3D[gi0], x0, y0, z0);
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
if (t1 < 0)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * Dot(m_gradiant3D[gi1], x1, y1, z1);
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
if (t2 < 0)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * Dot(m_gradiant3D[gi2], x2, y2, z2);
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
if (t3 < 0)
{
n3 = 0.0f;
}
else
{
t3 *= t3;
n3 = t3 * t3 * Dot(m_gradiant3D[gi3], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0f*(n0 + n1 + n2 + n3);
}
//-----------------------------------------------------------------------------------------------
// Perlin noise is fractal noise with "gradient vector smoothing" applied.
//
// In 4D, gradients are unit-length hyper-vectors in random (4D) directions.
//
float Compute4dPerlinNoise( float posX, float posY, float posZ, float posT, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
const Vector4 gradients[ 16 ] = // Hard to tell if this is any better in 4D than just having 8
{
Vector4( +0.5f, +0.5f, +0.5f, +0.5f ), // Normalized unit 4D vectors pointing toward each
Vector4( -0.5f, +0.5f, +0.5f, +0.5f ), // of the 16 hypercube corners, so components are
Vector4( +0.5f, -0.5f, +0.5f, +0.5f ), // all sqrt(4)/4, i.e. one-half.
Vector4( -0.5f, -0.5f, +0.5f, +0.5f ), //
Vector4( +0.5f, +0.5f, -0.5f, +0.5f ), // It's hard to tell whether these are any better
Vector4( -0.5f, +0.5f, -0.5f, +0.5f ), // or worse than vectors facing axes (1,0,0,0) or
Vector4( +0.5f, -0.5f, -0.5f, +0.5f ), // 3D edges (.7,.7,0,0) or 4D edges (.57,.57,.57,0)
Vector4( -0.5f, -0.5f, -0.5f, +0.5f ), // but less-axial gradients looked a little better
Vector4( +0.5f, +0.5f, +0.5f, -0.5f ), // with 2D and 3D noise so I'm assuming this is as
Vector4( -0.5f, +0.5f, +0.5f, -0.5f ), // good or better as any other gradient-selection
Vector4( +0.5f, -0.5f, +0.5f, -0.5f ), // scheme (and is crazy-fast). *shrug*
Vector4( -0.5f, -0.5f, +0.5f, -0.5f ), //
Vector4( +0.5f, +0.5f, -0.5f, -0.5f ), // Plus, we want a power-of-two number of evenly-
Vector4( -0.5f, +0.5f, -0.5f, -0.5f ), // distributed gradients, so we can cheaply select
Vector4( +0.5f, -0.5f, -0.5f, -0.5f ), // one from bit-noise (use bit-mask, not modulus).
Vector4( -0.5f, -0.5f, -0.5f, -0.5f ) //
};
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float invScale = (1.f / scale);
Vector4 currentPos( posX * invScale, posY * invScale, posZ * invScale, posT * invScale );
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine random unit "gradient vectors" for 16 surrounding 4D (hypercube) cell corners
Vector4 cellMins( FastFloor( currentPos.x ), FastFloor( currentPos.y ), FastFloor( currentPos.z ), FastFloor( currentPos.w ) );
Vector4 cellMaxs( cellMins.x + 1.f, cellMins.y + 1.f, cellMins.z + 1.f, cellMins.w + 1.f );
int indexWestX = (int) cellMins.x;
int indexSouthY = (int) cellMins.y;
int indexBelowZ = (int) cellMins.z;
int indexBeforeT = (int) cellMins.w;
int indexEastX = indexWestX + 1;
int indexNorthY = indexSouthY + 1;
int indexAboveZ = indexBelowZ + 1;
int indexAfterT = indexBeforeT + 1;
// "BeforeBSW" stands for "BeforeBelowSouthWest" below (i.e. 4D hypercube mins), etc.
unsigned int noiseBeforeBSW = Get4dNoiseUint( indexWestX, indexSouthY, indexBelowZ, indexBeforeT, seed );
unsigned int noiseBeforeBSE = Get4dNoiseUint( indexEastX, indexSouthY, indexBelowZ, indexBeforeT, seed );
unsigned int noiseBeforeBNW = Get4dNoiseUint( indexWestX, indexNorthY, indexBelowZ, indexBeforeT, seed );
unsigned int noiseBeforeBNE = Get4dNoiseUint( indexEastX, indexNorthY, indexBelowZ, indexBeforeT, seed );
unsigned int noiseBeforeASW = Get4dNoiseUint( indexWestX, indexSouthY, indexAboveZ, indexBeforeT, seed );
unsigned int noiseBeforeASE = Get4dNoiseUint( indexEastX, indexSouthY, indexAboveZ, indexBeforeT, seed );
unsigned int noiseBeforeANW = Get4dNoiseUint( indexWestX, indexNorthY, indexAboveZ, indexBeforeT, seed );
unsigned int noiseBeforeANE = Get4dNoiseUint( indexEastX, indexNorthY, indexAboveZ, indexBeforeT, seed );
unsigned int noiseAfterBSW = Get4dNoiseUint( indexWestX, indexSouthY, indexBelowZ, indexAfterT, seed );
unsigned int noiseAfterBSE = Get4dNoiseUint( indexEastX, indexSouthY, indexBelowZ, indexAfterT, seed );
unsigned int noiseAfterBNW = Get4dNoiseUint( indexWestX, indexNorthY, indexBelowZ, indexAfterT, seed );
unsigned int noiseAfterBNE = Get4dNoiseUint( indexEastX, indexNorthY, indexBelowZ, indexAfterT, seed );
unsigned int noiseAfterASW = Get4dNoiseUint( indexWestX, indexSouthY, indexAboveZ, indexAfterT, seed );
unsigned int noiseAfterASE = Get4dNoiseUint( indexEastX, indexSouthY, indexAboveZ, indexAfterT, seed );
unsigned int noiseAfterANW = Get4dNoiseUint( indexWestX, indexNorthY, indexAboveZ, indexAfterT, seed );
unsigned int noiseAfterANE = Get4dNoiseUint( indexEastX, indexNorthY, indexAboveZ, indexAfterT, seed );
Vector4 gradientBeforeBSW = gradients[ noiseBeforeBSW & 0x0000000F ];
Vector4 gradientBeforeBSE = gradients[ noiseBeforeBSE & 0x0000000F ];
Vector4 gradientBeforeBNW = gradients[ noiseBeforeBNW & 0x0000000F ];
Vector4 gradientBeforeBNE = gradients[ noiseBeforeBNE & 0x0000000F ];
Vector4 gradientBeforeASW = gradients[ noiseBeforeASW & 0x0000000F ];
Vector4 gradientBeforeASE = gradients[ noiseBeforeASE & 0x0000000F ];
Vector4 gradientBeforeANW = gradients[ noiseBeforeANW & 0x0000000F ];
Vector4 gradientBeforeANE = gradients[ noiseBeforeANE & 0x0000000F ];
Vector4 gradientAfterBSW = gradients[ noiseAfterBSW & 0x0000000F ];
Vector4 gradientAfterBSE = gradients[ noiseAfterBSE & 0x0000000F ];
Vector4 gradientAfterBNW = gradients[ noiseAfterBNW & 0x0000000F ];
Vector4 gradientAfterBNE = gradients[ noiseAfterBNE & 0x0000000F ];
Vector4 gradientAfterASW = gradients[ noiseAfterASW & 0x0000000F ];
Vector4 gradientAfterASE = gradients[ noiseAfterASE & 0x0000000F ];
Vector4 gradientAfterANW = gradients[ noiseAfterANW & 0x0000000F ];
Vector4 gradientAfterANE = gradients[ noiseAfterANE & 0x0000000F ];
// Dot each corner's gradient with displacement from corner to position
Vector4 displacementFromBeforeBSW( currentPos.x - cellMins.x, currentPos.y - cellMins.y, currentPos.z - cellMins.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeBSE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y, currentPos.z - cellMins.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeBNW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y, currentPos.z - cellMins.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeBNE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y, currentPos.z - cellMins.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeASW( currentPos.x - cellMins.x, currentPos.y - cellMins.y, currentPos.z - cellMaxs.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeASE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y, currentPos.z - cellMaxs.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeANW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y, currentPos.z - cellMaxs.z, currentPos.w - cellMins.w );
Vector4 displacementFromBeforeANE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y, currentPos.z - cellMaxs.z, currentPos.w - cellMins.w );
Vector4 displacementFromAfterBSW( currentPos.x - cellMins.x, currentPos.y - cellMins.y, currentPos.z - cellMins.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterBSE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y, currentPos.z - cellMins.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterBNW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y, currentPos.z - cellMins.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterBNE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y, currentPos.z - cellMins.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterASW( currentPos.x - cellMins.x, currentPos.y - cellMins.y, currentPos.z - cellMaxs.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterASE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y, currentPos.z - cellMaxs.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterANW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y, currentPos.z - cellMaxs.z, currentPos.w - cellMaxs.w );
Vector4 displacementFromAfterANE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y, currentPos.z - cellMaxs.z, currentPos.w - cellMaxs.w );
float dotBeforeBSW = MathUtils::Dot( gradientBeforeBSW, displacementFromBeforeBSW );
float dotBeforeBSE = MathUtils::Dot( gradientBeforeBSE, displacementFromBeforeBSE );
float dotBeforeBNW = MathUtils::Dot( gradientBeforeBNW, displacementFromBeforeBNW );
float dotBeforeBNE = MathUtils::Dot( gradientBeforeBNE, displacementFromBeforeBNE );
float dotBeforeASW = MathUtils::Dot( gradientBeforeASW, displacementFromBeforeASW );
float dotBeforeASE = MathUtils::Dot( gradientBeforeASE, displacementFromBeforeASE );
float dotBeforeANW = MathUtils::Dot( gradientBeforeANW, displacementFromBeforeANW );
float dotBeforeANE = MathUtils::Dot( gradientBeforeANE, displacementFromBeforeANE );
float dotAfterBSW = MathUtils::Dot( gradientAfterBSW, displacementFromAfterBSW );
float dotAfterBSE = MathUtils::Dot( gradientAfterBSE, displacementFromAfterBSE );
float dotAfterBNW = MathUtils::Dot( gradientAfterBNW, displacementFromAfterBNW );
float dotAfterBNE = MathUtils::Dot( gradientAfterBNE, displacementFromAfterBNE );
float dotAfterASW = MathUtils::Dot( gradientAfterASW, displacementFromAfterASW );
float dotAfterASE = MathUtils::Dot( gradientAfterASE, displacementFromAfterASE );
float dotAfterANW = MathUtils::Dot( gradientAfterANW, displacementFromAfterANW );
float dotAfterANE = MathUtils::Dot( gradientAfterANE, displacementFromAfterANE );
// Do a smoothed (nonlinear) weighted average of dot results
float weightEast = SmoothStep( displacementFromBeforeBSW.x );
float weightNorth = SmoothStep( displacementFromBeforeBSW.y );
float weightAbove = SmoothStep( displacementFromBeforeBSW.z );
float weightAfter = SmoothStep( displacementFromBeforeBSW.w );
float weightWest = 1.f - weightEast;
float weightSouth = 1.f - weightNorth;
float weightBelow = 1.f - weightAbove;
float weightBefore = 1.f - weightAfter;
// 16-way blend (16 -> 8 -> 4 -> 2 -> 1)
float blendBeforeBelowSouth = (weightEast * dotBeforeBSE) + (weightWest * dotBeforeBSW);
float blendBeforeBelowNorth = (weightEast * dotBeforeBNE) + (weightWest * dotBeforeBNW);
float blendBeforeAboveSouth = (weightEast * dotBeforeASE) + (weightWest * dotBeforeASW);
float blendBeforeAboveNorth = (weightEast * dotBeforeANE) + (weightWest * dotBeforeANW);
float blendAfterBelowSouth = (weightEast * dotAfterBSE) + (weightWest * dotAfterBSW);
float blendAfterBelowNorth = (weightEast * dotAfterBNE) + (weightWest * dotAfterBNW);
float blendAfterAboveSouth = (weightEast * dotAfterASE) + (weightWest * dotAfterASW);
float blendAfterAboveNorth = (weightEast * dotAfterANE) + (weightWest * dotAfterANW);
float blendBeforeBelow = (weightSouth * blendBeforeBelowSouth) + (weightNorth * blendBeforeBelowNorth);
float blendBeforeAbove = (weightSouth * blendBeforeAboveSouth) + (weightNorth * blendBeforeAboveNorth);
float blendAfterBelow = (weightSouth * blendAfterBelowSouth) + (weightNorth * blendAfterBelowNorth);
float blendAfterAbove = (weightSouth * blendAfterAboveSouth) + (weightNorth * blendAfterAboveNorth);
float blendBefore = (weightBelow * blendBeforeBelow) + (weightAbove * blendBeforeAbove);
float blendAfter = (weightBelow * blendAfterBelow) + (weightAbove * blendAfterAbove);
float blendTotal = (weightBefore * blendBefore) + (weightAfter * blendAfter);
float noiseThisOctave = 1.6f * blendTotal; // 4D Perlin is in ~[-.5,.5]; map to ~[-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPos *= octaveScale;
currentPos.x += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
currentPos.y += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
currentPos.z += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
currentPos.w += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
//-----------------------------------------------------------------------------------------------
// Perlin noise is fractal noise with "gradient vector smoothing" applied.
//
// In 3D, gradients are unit-length vectors in random (3D) directions.
//
float Compute3dPerlinNoise( float posX, float posY, float posZ, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
const Vector3 gradients[ 8 ] = // Traditional "12 edges" requires modulus and isn't any better.
{
Vector3( +fSQRT_3_OVER_3, +fSQRT_3_OVER_3, +fSQRT_3_OVER_3 ), // Normalized unit 3D vectors
Vector3( -fSQRT_3_OVER_3, +fSQRT_3_OVER_3, +fSQRT_3_OVER_3 ), // pointing toward cube
Vector3( +fSQRT_3_OVER_3, -fSQRT_3_OVER_3, +fSQRT_3_OVER_3 ), // corners, so components
Vector3( -fSQRT_3_OVER_3, -fSQRT_3_OVER_3, +fSQRT_3_OVER_3 ), // are all sqrt(3)/3, i.e.
Vector3( +fSQRT_3_OVER_3, +fSQRT_3_OVER_3, -fSQRT_3_OVER_3 ), // 0.5773502691896257645091f.
Vector3( -fSQRT_3_OVER_3, +fSQRT_3_OVER_3, -fSQRT_3_OVER_3 ), // These are slightly better
Vector3( +fSQRT_3_OVER_3, -fSQRT_3_OVER_3, -fSQRT_3_OVER_3 ), // than axes (1,0,0) and much
Vector3( -fSQRT_3_OVER_3, -fSQRT_3_OVER_3, -fSQRT_3_OVER_3 ) // faster than edges (1,1,0).
};
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float invScale = (1.f / scale);
Vector3 currentPos( posX * invScale, posY * invScale, posZ * invScale );
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine random unit "gradient vectors" for surrounding corners
Vector3 cellMins( FastFloor( currentPos.x ), FastFloor( currentPos.y ), FastFloor( currentPos.z ) );
Vector3 cellMaxs( cellMins.x + 1.f, cellMins.y + 1.f, cellMins.z + 1.f );
int indexWestX = (int) cellMins.x;
int indexSouthY = (int) cellMins.y;
int indexBelowZ = (int) cellMins.z;
int indexEastX = indexWestX + 1;
int indexNorthY = indexSouthY + 1;
int indexAboveZ = indexBelowZ + 1;
unsigned int noiseBelowSW = Get3dNoiseUint( indexWestX, indexSouthY, indexBelowZ, seed );
unsigned int noiseBelowSE = Get3dNoiseUint( indexEastX, indexSouthY, indexBelowZ, seed );
unsigned int noiseBelowNW = Get3dNoiseUint( indexWestX, indexNorthY, indexBelowZ, seed );
unsigned int noiseBelowNE = Get3dNoiseUint( indexEastX, indexNorthY, indexBelowZ, seed );
unsigned int noiseAboveSW = Get3dNoiseUint( indexWestX, indexSouthY, indexAboveZ, seed );
unsigned int noiseAboveSE = Get3dNoiseUint( indexEastX, indexSouthY, indexAboveZ, seed );
unsigned int noiseAboveNW = Get3dNoiseUint( indexWestX, indexNorthY, indexAboveZ, seed );
unsigned int noiseAboveNE = Get3dNoiseUint( indexEastX, indexNorthY, indexAboveZ, seed );
Vector3 gradientBelowSW = gradients[ noiseBelowSW & 0x00000007 ];
Vector3 gradientBelowSE = gradients[ noiseBelowSE & 0x00000007 ];
Vector3 gradientBelowNW = gradients[ noiseBelowNW & 0x00000007 ];
Vector3 gradientBelowNE = gradients[ noiseBelowNE & 0x00000007 ];
Vector3 gradientAboveSW = gradients[ noiseAboveSW & 0x00000007 ];
Vector3 gradientAboveSE = gradients[ noiseAboveSE & 0x00000007 ];
Vector3 gradientAboveNW = gradients[ noiseAboveNW & 0x00000007 ];
Vector3 gradientAboveNE = gradients[ noiseAboveNE & 0x00000007 ];
// Dot each corner's gradient with displacement from corner to position
Vector3 displacementFromBelowSW( currentPos.x - cellMins.x, currentPos.y - cellMins.y, currentPos.z - cellMins.z );
Vector3 displacementFromBelowSE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y, currentPos.z - cellMins.z );
Vector3 displacementFromBelowNW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y, currentPos.z - cellMins.z );
Vector3 displacementFromBelowNE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y, currentPos.z - cellMins.z );
Vector3 displacementFromAboveSW( currentPos.x - cellMins.x, currentPos.y - cellMins.y, currentPos.z - cellMaxs.z );
Vector3 displacementFromAboveSE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y, currentPos.z - cellMaxs.z );
Vector3 displacementFromAboveNW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y, currentPos.z - cellMaxs.z );
Vector3 displacementFromAboveNE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y, currentPos.z - cellMaxs.z );
float dotBelowSW = MathUtils::Dot( gradientBelowSW, displacementFromBelowSW );
float dotBelowSE = MathUtils::Dot( gradientBelowSE, displacementFromBelowSE );
float dotBelowNW = MathUtils::Dot( gradientBelowNW, displacementFromBelowNW );
float dotBelowNE = MathUtils::Dot( gradientBelowNE, displacementFromBelowNE );
float dotAboveSW = MathUtils::Dot( gradientAboveSW, displacementFromAboveSW );
float dotAboveSE = MathUtils::Dot( gradientAboveSE, displacementFromAboveSE );
float dotAboveNW = MathUtils::Dot( gradientAboveNW, displacementFromAboveNW );
float dotAboveNE = MathUtils::Dot( gradientAboveNE, displacementFromAboveNE );
// Do a smoothed (nonlinear) weighted average of dot results
float weightEast = SmoothStep5( displacementFromBelowSW.x );
float weightNorth = SmoothStep5( displacementFromBelowSW.y );
float weightAbove = SmoothStep5( displacementFromBelowSW.z );
float weightWest = 1.f - weightEast;
float weightSouth = 1.f - weightNorth;
float weightBelow = 1.f - weightAbove;
// 8-way blend (8 -> 4 -> 2 -> 1)
float blendBelowSouth = (weightEast * dotBelowSE) + (weightWest * dotBelowSW);
float blendBelowNorth = (weightEast * dotBelowNE) + (weightWest * dotBelowNW);
float blendAboveSouth = (weightEast * dotAboveSE) + (weightWest * dotAboveSW);
float blendAboveNorth = (weightEast * dotAboveNE) + (weightWest * dotAboveNW);
float blendBelow = (weightSouth * blendBelowSouth) + (weightNorth * blendBelowNorth);
float blendAbove = (weightSouth * blendAboveSouth) + (weightNorth * blendAboveNorth);
float blendTotal = (weightBelow * blendBelow) + (weightAbove * blendAbove);
float noiseThisOctave = 1.66666666f * blendTotal; // 3D Perlin is ~[-.6,.6]; map to ~[-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPos *= octaveScale;
currentPos.x += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
currentPos.y += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
currentPos.z += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
//-----------------------------------------------------------------------------------------------
// Perlin noise is fractal noise with "gradient vector smoothing" applied.
//
// In 2D, gradients are unit-length vectors in various directions with even angular distribution.
//
float Compute2dPerlinNoise( float posX, float posY, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
const Vector2 gradients[ 8 ] = // Normalized unit vectors in 8 quarter-cardinal directions
{
Vector2( +0.923879533f, +0.382683432f ), // 22.5 degrees
Vector2( +0.382683432f, +0.923879533f ), // 67.5 degrees
Vector2( -0.382683432f, +0.923879533f ), // 112.5 degrees
Vector2( -0.923879533f, +0.382683432f ), // 157.5 degrees
Vector2( -0.923879533f, -0.382683432f ), // 202.5 degrees
Vector2( -0.382683432f, -0.923879533f ), // 247.5 degrees
Vector2( +0.382683432f, -0.923879533f ), // 292.5 degrees
Vector2( +0.923879533f, -0.382683432f ) // 337.5 degrees
};
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float invScale = (1.f / scale);
Vector2 currentPos( posX * invScale, posY * invScale );
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine random unit "gradient vectors" for surrounding corners
Vector2 cellMins( FastFloor( currentPos.x ), FastFloor( currentPos.y ) );
Vector2 cellMaxs( cellMins.x + 1.f, cellMins.y + 1.f );
int indexWestX = (int) cellMins.x;
int indexSouthY = (int) cellMins.y;
int indexEastX = indexWestX + 1;
int indexNorthY = indexSouthY + 1;
unsigned int noiseSW = Get2dNoiseUint( indexWestX, indexSouthY, seed );
unsigned int noiseSE = Get2dNoiseUint( indexEastX, indexSouthY, seed );
unsigned int noiseNW = Get2dNoiseUint( indexWestX, indexNorthY, seed );
unsigned int noiseNE = Get2dNoiseUint( indexEastX, indexNorthY, seed );
Vector2 gradientSW = gradients[ noiseSW & 0x00000007 ];
Vector2 gradientSE = gradients[ noiseSE & 0x00000007 ];
Vector2 gradientNW = gradients[ noiseNW & 0x00000007 ];
Vector2 gradientNE = gradients[ noiseNE & 0x00000007 ];
// Dot each corner's gradient with displacement from corner to position
Vector2 displacementFromSW( currentPos.x - cellMins.x, currentPos.y - cellMins.y );
Vector2 displacementFromSE( currentPos.x - cellMaxs.x, currentPos.y - cellMins.y );
Vector2 displacementFromNW( currentPos.x - cellMins.x, currentPos.y - cellMaxs.y );
Vector2 displacementFromNE( currentPos.x - cellMaxs.x, currentPos.y - cellMaxs.y );
float dotSouthWest = MathUtils::Dot( gradientSW, displacementFromSW );
float dotSouthEast = MathUtils::Dot( gradientSE, displacementFromSE );
float dotNorthWest = MathUtils::Dot( gradientNW, displacementFromNW );
float dotNorthEast = MathUtils::Dot( gradientNE, displacementFromNE );
// Do a smoothed (nonlinear) weighted average of dot results
float weightEast = SmoothStep5( displacementFromSW.x );
float weightNorth = SmoothStep5( displacementFromSW.y );
float weightWest = 1.f - weightEast;
float weightSouth = 1.f - weightNorth;
float blendSouth = (weightEast * dotSouthEast) + (weightWest * dotSouthWest);
float blendNorth = (weightEast * dotNorthEast) + (weightWest * dotNorthWest);
float blendTotal = (weightSouth * blendSouth) + (weightNorth * blendNorth);
float noiseThisOctave = 1.5f * blendTotal; // 2D Perlin is in ~[-.66,.66]; map to ~[-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPos *= octaveScale;
currentPos.x += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
currentPos.y += OCTAVE_OFFSET; // Add "irrational" offset to de-align octave grids
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
//-----------------------------------------------------------------------------------------------
float Compute4dFractalNoise( float posX, float posY, float posZ, float posT, float scale, unsigned int numOctaves, float octavePersistence, float octaveScale, bool renormalize, unsigned int seed )
{
const float OCTAVE_OFFSET = 0.636764989593174f; // Translation/bias to add to each octave
float totalNoise = 0.f;
float totalAmplitude = 0.f;
float currentAmplitude = 1.f;
float invScale = (1.f / scale);
Vector4 currentPos( posX * invScale, posY * invScale, posZ * invScale, posT * invScale );
for( unsigned int octaveNum = 0; octaveNum < numOctaves; ++ octaveNum )
{
// Determine noise values at nearby integer "grid point" positions
Vector4 cellMins( FastFloor( currentPos.x ), FastFloor( currentPos.y ), FastFloor( currentPos.z ), FastFloor( currentPos.w ) );
int indexWestX = (int) cellMins.x;
int indexSouthY = (int) cellMins.y;
int indexBelowZ = (int) cellMins.z;
int indexBeforeT = (int) cellMins.w;
int indexEastX = indexWestX + 1;
int indexNorthY = indexSouthY + 1;
int indexAboveZ = indexBelowZ + 1;
int indexAfterT = indexBeforeT + 1;
// Noise grid cell has 16 "corners" in 4D
float beforeBelowSW = Get4dNoiseZeroToOne( indexWestX, indexSouthY, indexBelowZ, indexBeforeT, seed );
float beforeBelowSE = Get4dNoiseZeroToOne( indexEastX, indexSouthY, indexBelowZ, indexBeforeT, seed );
float beforeBelowNW = Get4dNoiseZeroToOne( indexWestX, indexNorthY, indexBelowZ, indexBeforeT, seed );
float beforeBelowNE = Get4dNoiseZeroToOne( indexEastX, indexNorthY, indexBelowZ, indexBeforeT, seed );
float beforeAboveSW = Get4dNoiseZeroToOne( indexWestX, indexSouthY, indexAboveZ, indexBeforeT, seed );
float beforeAboveSE = Get4dNoiseZeroToOne( indexEastX, indexSouthY, indexAboveZ, indexBeforeT, seed );
float beforeAboveNW = Get4dNoiseZeroToOne( indexWestX, indexNorthY, indexAboveZ, indexBeforeT, seed );
float beforeAboveNE = Get4dNoiseZeroToOne( indexEastX, indexNorthY, indexAboveZ, indexBeforeT, seed );
float afterBelowSW = Get4dNoiseZeroToOne( indexWestX, indexSouthY, indexBelowZ, indexAfterT, seed );
float afterBelowSE = Get4dNoiseZeroToOne( indexEastX, indexSouthY, indexBelowZ, indexAfterT, seed );
float afterBelowNW = Get4dNoiseZeroToOne( indexWestX, indexNorthY, indexBelowZ, indexAfterT, seed );
float afterBelowNE = Get4dNoiseZeroToOne( indexEastX, indexNorthY, indexBelowZ, indexAfterT, seed );
float afterAboveSW = Get4dNoiseZeroToOne( indexWestX, indexSouthY, indexAboveZ, indexAfterT, seed );
float afterAboveSE = Get4dNoiseZeroToOne( indexEastX, indexSouthY, indexAboveZ, indexAfterT, seed );
float afterAboveNW = Get4dNoiseZeroToOne( indexWestX, indexNorthY, indexAboveZ, indexAfterT, seed );
float afterAboveNE = Get4dNoiseZeroToOne( indexEastX, indexNorthY, indexAboveZ, indexAfterT, seed );
// Do a smoothed (nonlinear) weighted average of nearby grid point values
Vector4 displacementFromMins = currentPos - cellMins;
float weightEast = SmoothStep( displacementFromMins.x );
float weightNorth = SmoothStep( displacementFromMins.y );
float weightAbove = SmoothStep( displacementFromMins.z );
float weightAfter = SmoothStep( displacementFromMins.w );
float weightWest = 1.f - weightEast;
float weightSouth = 1.f - weightNorth;
float weightBelow = 1.f - weightAbove;
float weightBefore = 1.f - weightAfter;
// 16-way blend (16 -> 8 -> 4 -> 2 -> 1)
float blendBeforeBelowSouth = (weightEast * beforeBelowSE) + (weightWest * beforeBelowSW);
float blendBeforeBelowNorth = (weightEast * beforeBelowNE) + (weightWest * beforeBelowNW);
float blendBeforeAboveSouth = (weightEast * beforeAboveSE) + (weightWest * beforeAboveSW);
float blendBeforeAboveNorth = (weightEast * beforeAboveNE) + (weightWest * beforeAboveNW);
float blendAfterBelowSouth = (weightEast * afterBelowSE) + (weightWest * afterBelowSW);
float blendAfterBelowNorth = (weightEast * afterBelowNE) + (weightWest * afterBelowNW);
float blendAfterAboveSouth = (weightEast * afterAboveSE) + (weightWest * afterAboveSW);
float blendAfterAboveNorth = (weightEast * afterAboveNE) + (weightWest * afterAboveNW);
float blendBeforeBelow = (weightSouth * blendBeforeBelowSouth) + (weightNorth * blendBeforeBelowNorth);
float blendBeforeAbove = (weightSouth * blendBeforeAboveSouth) + (weightNorth * blendBeforeAboveNorth);
float blendAfterBelow = (weightSouth * blendAfterBelowSouth) + (weightNorth * blendAfterBelowNorth);
float blendAfterAbove = (weightSouth * blendAfterAboveSouth) + (weightNorth * blendAfterAboveNorth);
float blendBefore = (weightBelow * blendBeforeBelow) + (weightAbove * blendBeforeAbove);
float blendAfter = (weightBelow * blendAfterBelow) + (weightAbove * blendAfterAbove);
float blendTotal = (weightBefore * blendBefore) + (weightAfter * blendAfter);
float noiseThisOctave = 2.f * (blendTotal - 0.5f); // Map from [0,1] to [-1,1]
// Accumulate results and prepare for next octave (if any)
totalNoise += noiseThisOctave * currentAmplitude;
totalAmplitude += currentAmplitude;
currentAmplitude *= octavePersistence;
currentPos *= octaveScale;
currentPos.x += OCTAVE_OFFSET; // Add "irrational" offsets to noise position components
currentPos.y += OCTAVE_OFFSET; // at each octave to break up their grid alignment
currentPos.z += OCTAVE_OFFSET;
currentPos.w += OCTAVE_OFFSET;
++ seed; // Eliminates octaves "echoing" each other (since each octave is uniquely seeded)
}
// Re-normalize total noise to within [-1,1] and fix octaves pulling us far away from limits
if( renormalize && totalAmplitude > 0.f )
{
totalNoise /= totalAmplitude; // Amplitude exceeds 1.0 if octaves are used
totalNoise = (totalNoise * 0.5f) + 0.5f; // Map to [0,1]
totalNoise = SmoothStep( totalNoise ); // Push towards extents (octaves pull us away)
totalNoise = (totalNoise * 2.0f) - 1.f; // Map back to [-1,1]
}
return totalNoise;
}
//
// 获得光照参数
//
BOOL CLightGrid::GetLightParams(DWORD dwChannel, const VEC3 *position, VEC4 *direction, VEC3 *ambient, VEC3 *diffuse, VEC3 *specular, VEC3 *rim, VEC3 *skyLower, VEC3 *skyUpper, VEC3 *indirectUp, VEC3 *indirectDown, VEC3 *indirectLeft, VEC3 *indirectRight, VEC3 *indirectFront, VEC3 *indirectBack) const
{
ASSERT(position);
//
// 1. 通道检查
//
if ((LIGHT_CHANNEL & dwChannel) == 0) {
return FALSE;
}
//
// 2. 获得光照参数
//
for (LightVolumeSet::const_iterator itVolume = m_volumes.begin(); itVolume != m_volumes.end(); ++itVolume) {
const LIGHT_VOLUME *pVolume = *itVolume;
ASSERT(pVolume);
if (IsPointInAABB(&pVolume->aabb, (*position)[0], (*position)[1], (*position)[2])) {
FLOAT posx = ((*position)[0] - pVolume->aabb.minVertex[0]) / pVolume->stepx;
FLOAT posy = ((*position)[1] - pVolume->aabb.minVertex[1]) / pVolume->stepy;
FLOAT posz = ((*position)[2] - pVolume->aabb.minVertex[2]) / pVolume->stepz;
INT x = FastFloor(posx);
INT y = FastFloor(posy);
INT z = FastFloor(posz);
FLOAT factor;
FLOAT factorx = posx - x;
FLOAT factory = posy - y;
FLOAT factorz = posz - z;
VEC3 _direction;
VEC3 _ambient;
VEC3 _diffuse;
VEC3 _indirectUp;
VEC3 _indirectDown;
VEC3 _indirectLeft;
VEC3 _indirectRight;
VEC3 _indirectFront;
VEC3 _indirectBack;
Vec3Zero(&_direction);
Vec3Zero(&_ambient);
Vec3Zero(&_diffuse);
Vec3Zero(&_indirectUp);
Vec3Zero(&_indirectDown);
Vec3Zero(&_indirectLeft);
Vec3Zero(&_indirectRight);
Vec3Zero(&_indirectFront);
Vec3Zero(&_indirectBack);
for (INT xx = 0; xx <= 1; xx++) {
factorx = 1.0f - factorx;
for (INT yy = 0; yy <= 1; yy++) {
factory = 1.0f - factory;
for (INT zz = 0; zz <= 1; zz++) {
factorz = 1.0f - factorz;
factor = factorx * factory * factorz;
if (LIGHT_POINT *pLightPoint = &pVolume->pppLightPoints[x + xx][y + yy][z + zz]) {
VEC3 __direction;
VEC3 __ambient;
VEC3 __diffuse;
VEC3 __indirectUp;
VEC3 __indirectDown;
VEC3 __indirectLeft;
VEC3 __indirectRight;
VEC3 __indirectFront;
VEC3 __indirectBack;
Vec3LatLongToDirection(&__direction, pLightPoint->direction);
Vec3BytesToColor(&__ambient, pLightPoint->ambient);
Vec3BytesToColor(&__diffuse, pLightPoint->diffuse);
Vec3BytesToColor(&__indirectUp, pLightPoint->indirectup);
Vec3BytesToColor(&__indirectDown, pLightPoint->indirectdown);
Vec3BytesToColor(&__indirectLeft, pLightPoint->indirectleft);
Vec3BytesToColor(&__indirectRight, pLightPoint->indirectright);
Vec3BytesToColor(&__indirectFront, pLightPoint->indirectfront);
Vec3BytesToColor(&__indirectBack, pLightPoint->indirectback);
Vec3Ma(&_direction, &_direction, &__direction, factor);
Vec3Ma(&_ambient, &_ambient, &__ambient, factor);
Vec3Ma(&_diffuse, &_diffuse, &__diffuse, factor);
Vec3Ma(&_indirectUp, &_diffuse, &__indirectUp, factor);
Vec3Ma(&_indirectDown, &_diffuse, &__indirectDown, factor);
Vec3Ma(&_indirectLeft, &_diffuse, &__indirectLeft, factor);
Vec3Ma(&_indirectRight, &_diffuse, &__indirectRight, factor);
Vec3Ma(&_indirectFront, &_diffuse, &__indirectFront, factor);
Vec3Ma(&_indirectBack, &_diffuse, &__indirectBack, factor);
}
}
}
}
Vec3Normalize(&_direction);
Vec3Clamp(&_ambient);
Vec3Clamp(&_diffuse);
Vec3Clamp(&_indirectUp);
Vec3Clamp(&_indirectDown);
Vec3Clamp(&_indirectLeft);
Vec3Clamp(&_indirectRight);
Vec3Clamp(&_indirectFront);
Vec3Clamp(&_indirectBack);
static const FLOAT specularFactor = 0.8f;
static const FLOAT rimFactor = 0.2f;
static const FLOAT skyLowerFactor = 0.2f;
static const FLOAT skyUpperFactor = 0.4f;
if (direction) Vec4Set(direction, _direction[0], _direction[1], _direction[2], 0.0f);
if (ambient) Vec3Set(ambient, _ambient[0], _ambient[1], _ambient[2]);
if (diffuse) Vec3Set(diffuse, _diffuse[0], _diffuse[1], _diffuse[2]);
if (specular) Vec3Set(specular, specularFactor * _diffuse[0], specularFactor * _diffuse[1], specularFactor * _diffuse[2]);
if (rim) Vec3Set(rim, rimFactor * _diffuse[0], rimFactor * _diffuse[1], rimFactor * _diffuse[2]);
if (skyLower) Vec3Set(skyLower, skyLowerFactor * _diffuse[0], skyLowerFactor * _diffuse[1], skyLowerFactor * _diffuse[2]);
if (skyUpper) Vec3Set(skyUpper, skyUpperFactor * _diffuse[0], skyUpperFactor * _diffuse[1], skyUpperFactor * _diffuse[2]);
if (indirectUp) Vec3Set(indirectUp, _indirectUp[0], _indirectUp[1], _indirectUp[2]);
if (indirectDown) Vec3Set(indirectDown, _indirectDown[0], _indirectDown[1], _indirectDown[2]);
if (indirectLeft) Vec3Set(indirectLeft, _indirectLeft[0], _indirectLeft[1], _indirectLeft[2]);
if (indirectRight) Vec3Set(indirectRight, _indirectRight[0], _indirectRight[1], _indirectRight[2]);
if (indirectFront) Vec3Set(indirectFront, _indirectFront[0], _indirectFront[1], _indirectFront[2]);
if (indirectBack) Vec3Set(indirectBack, _indirectBack[0], _indirectBack[1], _indirectBack[2]);
return TRUE;
}
}
return FALSE;
}
