slang_library_noise.c

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      t2 *= t2;
      n2 = t2 * t2 * grad2(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! */
}

/* 3D simplex noise */
GLfloat _slang_library_noise3 (GLfloat x, GLfloat y, GLfloat z)
{
/* Simple skewing factors for the 3D case */
#define F3 0.333333333f
#define G3 0.166666667f

    float n0, n1, n2, n3; /* Noise contributions from the four corners */

    /* Skew the input space to determine which simplex cell we're in */
    float s = (x+y+z)*F3; /* Very nice and simple skew factor for 3D */
    float xs = x+s;
    float ys = y+s;
    float zs = z+s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);
    int k = FASTFLOOR(zs);

    float t = (float)(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;

    float x1, y1, z1, x2, y2, z2, x3, y3, z3;
    int ii, jj, kk;
    float t0, t1, t2, t3;

    /* 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 */

/* This code would benefit from a backport from the GLSL version! */
    if(x0>=y0) {
      if(y0>=z0)
        { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } /* X Y Z order */
        else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } /* X Z Y order */
        else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } /* Z X Y order */
      }
    else { /* x0<y0 */
      if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } /* Z Y X order */
      else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } /* Y Z X order */
      else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } /* Y X Z order */
    }

    /* 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. */

    x1 = x0 - i1 + G3; /* Offsets for second corner in (x,y,z) coords */
    y1 = y0 - j1 + G3;
    z1 = z0 - k1 + G3;
    x2 = x0 - i2 + 2.0f*G3; /* Offsets for third corner in (x,y,z) coords */
    y2 = y0 - j2 + 2.0f*G3;
    z2 = z0 - k2 + 2.0f*G3;
    x3 = x0 - 1.0f + 3.0f*G3; /* Offsets for last corner in (x,y,z) coords */
    y3 = y0 - 1.0f + 3.0f*G3;
    z3 = z0 - 1.0f + 3.0f*G3;

    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
    ii = i % 256;
    jj = j % 256;
    kk = k % 256;

    /* Calculate the contribution from the four corners */
    t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad3(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
    }

    t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad3(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
    }

    t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad3(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
    }

    t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
    if(t3<0.0f) n3 = 0.0f;
    else {
      t3 *= t3;
      n3 = t3 * t3 * grad3(perm[ii+1+perm[jj+1+perm[kk+1]]], 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); /* TODO: The scale factor is preliminary! */
}

/* 4D simplex noise */
GLfloat _slang_library_noise4 (GLfloat x, GLfloat y, GLfloat z, GLfloat w)
{
  /* The skewing and unskewing factors are hairy again for the 4D case */
#define F4 0.309016994f /* F4 = (Math.sqrt(5.0)-1.0)/4.0 */
#define G4 0.138196601f /* G4 = (5.0-Math.sqrt(5.0))/20.0 */

    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 */
    float xs = x + s;
    float ys = y + s;
    float zs = z + s;
    float ws = w + s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);
    int k = FASTFLOOR(zs);
    int l = FASTFLOOR(ws);

    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 */

    float x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3, x4, y4, z4, w4;
    int ii, jj, kk, ll;
    float t0, t1, t2, t3, t4;

    /* 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 = simplex[c][0]>=3 ? 1 : 0;
    j1 = simplex[c][1]>=3 ? 1 : 0;
    k1 = simplex[c][2]>=3 ? 1 : 0;
    l1 = simplex[c][3]>=3 ? 1 : 0;
    /* The number 2 in the "simplex" array is at the second largest coordinate. */
    i2 = simplex[c][0]>=2 ? 1 : 0;
    j2 = simplex[c][1]>=2 ? 1 : 0;
    k2 = simplex[c][2]>=2 ? 1 : 0;
    l2 = simplex[c][3]>=2 ? 1 : 0;
    /* The number 1 in the "simplex" array is at the second smallest coordinate. */
    i3 = simplex[c][0]>=1 ? 1 : 0;
    j3 = simplex[c][1]>=1 ? 1 : 0;
    k3 = simplex[c][2]>=1 ? 1 : 0;
    l3 = simplex[c][3]>=1 ? 1 : 0;
    /* The fifth corner has all coordinate offsets = 1, so no need to look that up. */

    x1 = x0 - i1 + G4; /* Offsets for second corner in (x,y,z,w) coords */
    y1 = y0 - j1 + G4;
    z1 = z0 - k1 + G4;
    w1 = w0 - l1 + G4;
    x2 = x0 - i2 + 2.0f*G4; /* Offsets for third corner in (x,y,z,w) coords */
    y2 = y0 - j2 + 2.0f*G4;
    z2 = z0 - k2 + 2.0f*G4;
    w2 = w0 - l2 + 2.0f*G4;
    x3 = x0 - i3 + 3.0f*G4; /* Offsets for fourth corner in (x,y,z,w) coords */
    y3 = y0 - j3 + 3.0f*G4;
    z3 = z0 - k3 + 3.0f*G4;
    w3 = w0 - l3 + 3.0f*G4;
    x4 = x0 - 1.0f + 4.0f*G4; /* Offsets for last corner in (x,y,z,w) coords */
    y4 = y0 - 1.0f + 4.0f*G4;
    z4 = z0 - 1.0f + 4.0f*G4;
    w4 = w0 - 1.0f + 4.0f*G4;

    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
    ii = i % 256;
    jj = j % 256;
    kk = k % 256;
    ll = l % 256;

    /* Calculate the contribution from the five corners */
    t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
    }

   t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
    }

   t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
    }

   t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
    if(t3 < 0.0f) n3 = 0.0f;
    else {
      t3 *= t3;
      n3 = t3 * t3 * grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
    }

   t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
    if(t4 < 0.0f) n4 = 0.0f;
    else {
      t4 *= t4;
      n4 = t4 * t4 * grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4);
    }

    /* Sum up and scale the result to cover the range [-1,1] */
    return 27.0f * (n0 + n1 + n2 + n3 + n4); /* TODO: The scale factor is preliminary! */
}