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Catalog of Variations
Scott Draves edited this page May 16, 2015
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##Catalog of Variations
The variations are used as follows:
- An initial affine transformation of the input point (x,y) is done using the 'coefs' part of the transform. This results in a new set of coordinates, (X,Y).
- The (X,Y) coordinates are used to feed each of the different variations selected in the xform.
- The contribution of each weighted variation is added together to generate a third set of coordinates, (X',Y').
- If there is a post transform present in the xform, an additional affine transform based on the 'post' coefs in the xform is performed on (X',Y').
While most of the variations rely solely on the input coordinates (X,Y) for their output, some are 'parameterized' as noted.
(X,Y) will be used for the input coordinates. W will be used for the variation weight. (Vx,Vy) will be used for post-variation coordinates.
(0) Linear
Vx = W * X;
Vy = W * Y;
(1) Sinusoidal
Vx = W * sin(X);
Vy = W * sin(Y);
(2) Spherical
r2 = 1 / (X^2 + Y^2 + 1e-6);
Vx = W * X * r2;
Vy = W * Y * r2;
(3) Swirl
r2 = X^2 + Y^2;
c1 = sin(r2);
c2 = cos(r2);
Vx = W * (c1 * X - c2 * Y);
Vy = W * (c2 * X + c1 * Y);
(4) Horseshoe
r = 1 / (sqrt(X^2 + Y^2) + EPS);
Vx = W * (X-Y) * (X+Y) * r;
Vy = W * 2 * X * Y * r;
(5) Polar
r = sqrt(X^2 + Y^2);
a = atan2(X,Y);
Vx = W * a / PI;
Vy = W * (r - 1.0);
(6) Handkerchief
r = sqrt(X^2 + Y^2);
a = atan2(X,Y);
Vx = W * r * sin(a+r);
Vy = W * r * cos(a-r);
(7) Heart
a = atan2(X,Y) * sqrt(X^2 + Y^2);
r = W * sqrt(X^2 + Y^2);
Vx = r * sin(a);
Vy = (-r) * cos(a);
(8) Disc
a = atan2(X*PI,Y*PI) / PI;
r = PI * sqrt(X^2 + Y^2);
Vx = W * sin(r) * a;
Vy = W * cos(r) * a;
(9) Spiral
r = sqrt(X^2 + Y^2) + 1e-6;
a = atan2(X,Y);
r1 = W / r;
Vx = r1 * (cos(a) + sin(r));
Vy = r1 * (sin(a) - cos(r));
(10) Hyperbolic
r = sqrt(X^2 + Y^2) + 1e-6;
a = atan2(X,Y);
Vx = W * sin(a) / r;
Vy = W * cos(a) * r;
(11) Diamond
r = sqrt(X^2 + Y^2);
a = atan2(X,Y);
Vx = W * sin(a) * cos(r);
Vy = W * cos(a) * sin(r);
(12) Ex
a = atan2(X,Y);
r = sqrt(X^2 + Y^2);
n0 = sin(a+r);
n1 = cos(a-r);
m0 = r * n0^3;
m1 = r * n1^3;
Vx = W * (m0 + m1);
Vy = W * (m0 - m1);
(13) Julia
a = atan2(X,Y)/2;
if ( random_bit )
a += PI;
r = W * (X^2 + Y^2)^0.25;
Vx = r * cos(a);
Vy = r * sin(a);
(14) Bent
if (X < 0) X *= 2.0;
if (Y < 0) Y /= 2.0;
Vx = W * x;
Vy = W * y;
(15) Waves
nx = X + c(1,0) * sin(Y / (c(2,0)^2 + EPS));
ny = Y + c(1,1) * sin(X / (c(2,1)^2 + EPS));
Vx = W * nx;
Vy = W * ny;
(16) Fisheye
r = sqrt(X^2 + Y^2);
K = 2 * W / (r+1);
Vx = K * y;
Vy = K * x;
(17) Popcorn
dx = tan(3*Y);
dy = tan(3*X);
nx = X + c(2,0) * sin(dx);
ny = Y + c(2,1) * sin(dy);
Vx = W * nx;
Vy = W * ny;
(18) Exponential
dx = W * e^(X-1);
dy = PI * Y;
Vx = dx * cos(dy);
Vy = dx * sin(dy);
(19) Power
a = atan2(X,Y);
r = W * (sqrt(X^2 + Y^2))^sin(a);
Vx = r * cos(a);
Vy = r * sin(a);
(20) Cosine
nx = cos(X*PI) * cosh(Y);
ny = -sin(X*PI) * sinh(Y);
Vx = W * nx;
Vy = W * ny;
(21) Rings
dx = c(2,0)^2 + EPS;
r = sqrt(X^2 + Y^2);
a = atan2(X,Y);
rp = W * (fmod(r+dx,2*dx) - dx + r*(1-dx));
Vx = rp * cos(a);
Vy = rp * sin(a);
(22) Fan
dx = PI * (c(2,0)^2 + EPS);
dy = c(2,1);
dx2 = dx/2;
a = atan2(X,Y);
r = W * sqrt(X^2 + Y^2);
a += (fmod(a+dy,dx) > dx2) ? -dx2 : dx2;
Vx = r * cos(a);
Vy = r * sin(a);
(23) Eyefish
r = (2 * W) / (sqrt(X^2 + Y^2) + 1);
Vx = r * X;
Vy = r * Y;
(24) Bubble
r = W / ( (X^2 + Y^2)/4 + 1);
Vx = r * X;
Vy = r * Y;
(25) Cylinder
Vx = r * sin(X);
Vy = r * Y;
(26) Noise
r = W * random;
Vx = X * r * cos(random * 2 * PI);
Vy = Y * r * sin(random * 2 * PI);
(27) Blur
r = W * random;
Vx = r * cos(random * 2 * PI);
Vy = r * sin(random * 2 * PI);
(28) Rings2 (parameter: rings2_val)
r = sqrt(X^2 + Y^2);
a = atan2(X,Y);
dx = rings2_val^2 + EPS;
r += -2*dx*(int)((r+dx)/(2*dx)) + r*(1-dx);
Vx = W * sin(a) * r;
Vy = W * cos(a) * r;
(29) Fan2 (parameters: fan2_x, fan2_y)
dx = PI * (fan2_x^2 + EPS);
dx2 = dx / 2;
a = atan2(X,Y);
r = W * sqrt(X^2 + Y^2);
t = a+fan2_y - dx * (int)((a+fan2_y)/dx);
if (t>dx2)
a-=dx2;
else
a+=dx2;
Vx = r * sin(a);
Vy = r * cos(a);
(30) Blob (parameters: blob_high, blob_low, blob_waves)
r = sqrt(X^2 + Y^2);
a = atan2(X,Y);
bdiff = blob_high - blob_low;
r = r * (blob_low + bdiff * (1/2 + sin(blob_waves * a)/2));
Vx = W * sin(a) * r;
Vy = W * cos(a) * r;
(31) PDJ (parameters: pdj_a, pdj_b, pdj_c, pdj_d)
nx1 = cos(pdj_b * X);
nx2 = sin(pdj_c * X);
ny1 = sin(pdj_a * Y);
ny2 = cos(pdj_d * Y);
Vx = W * (ny1 - nx1);
Vy = W * (nx2 - ny2);
(32) Perspective (parameters: perspective_angle, perspective_dist)
vsin = sin(perspective_angle * PI / 2);
vfcos = W * perspective_dist * cos(perspective_angle * PI / 2);
t = (perspective_dist - X * vsin);
Vx = vf * X / t;
Vy = vfcos * Y / t;
(33) JuliaN (parameters: julian_power, julian_dist)
rN = abs(julian_power);
cn = julian_dist / julian_power / 2;
sina = sin((arctan2(Y, X) + 2 * PI * random(rN)) / N);
cosa = cos((arctan2(Y, X) + 2 * PI * random(rN)) / N);
r = W * Power(X * X + Y * Y, cn);
Vx = r * cosa;
Vy = r * sina;
(34) JuliaScope (parameters: juliascope_power, juliascope_dist)
rN = abs(juliascope_power);
cn = juliascope_dist / juliascope_power / 2;
rnd = random(rN);
if ((rnd and 1) = 0) {
sina = sin((2 * PI * rnd + arctan2(Y, X)) / juliascope_power);
cosa = cos((2 * PI * rnd + arctan2(Y, X)) / juliascope_power);
} else {
sina = sin((2 * PI * rnd - arctan2(Y, X)) / juliascope_power);
cosa = cos((2 * PI * rnd - arctan2(Y, X)) / juliascope_power);
}
r = W * Power (X * X + Y * Y, cN);
Vx = r * cosa;
Vy = r * sina;
(35) Blur
tmpr = random * 2 * PI;
sinr = sin(tmpr);
cosr = cos(tmpr);
r = W * random;
Vx = r * cosr;
Vy = r * sinr;
(36) Gaussian
ang = random * 2 * PI;
sina = sin(ang);
cosa = cos(ang);
r = W * (random + random + random + random - 2.0);
Vx = r * cosr;
Vy = r * sinr;
(37) RadialBlur (parameter: radialBlur_angle)
spinvar = sin(radialBlur_angle * PI / 2);
zoomvar = cos(radialBlur_angle * PI / 2);
rndG = W * (random + random + random + random - 2.0);
rA = sqrt(X^2 + Y^2);
tmpa = arctan2(Y, X) + spinvar*rndG;
sa = sin(tmpa);
ca = cos(tmpa);
rz = zoomvar * rndG - 1;
Vx = ra * ca + X*rz;
Vy = ra * sa + Y*rz;
(38) Pie (parameters: pie_slices, pie_rotation, pie_thickness)
sl = (int) (random * pie_slices + 0.5);
a = pie_rotation + 2 * PI * (sl + random * pie_thickness) / pie_slices;
r = W * random;
Vx = r * cos(a);
Vy = r * sin(a);
(39) Ngon (parameters: ngon_power, ngon_sides, ngon_corners, ngon_circle)
r_factor = Power(X^2 + Y^2, ngon_power/2.0);
theta = ArcTan2(Y,X);
b = 2 * PI / ngon_sides;
phi = theta - (b * floor(theta / b));
if (phi > b/2)
phi = phi - b;
amp = ngon_corners * (1.0 / (cos(phi) + EPS) - 1.0) + ngon_circle;
amp = amp / (r_factor + EPS);
Vx = W * X * amp;
Vy = W * Y * amp;
(40) Curl (parameters: curl_c1, curl_c2)
re = 1 + (c1 * X) + (c2 * X^2) - Y^2;
im = (c1 * Y) + (2 * c2 * X * Y);
r = W / (re^2 + im^2);
Vx = ((X * re) + (Y * im)) * r;
Vy = ((Y * re) - (X * im)) * r;
(41) Rectangles (parameters: rectangles_x, rectangles_y)
if rectangles_x==0
Vx = W * X;
else
Vx = W * ((2 * floor(X / rectangles_x) + 1) * rectangles_x - X);
if rectangles_y==0
Vy = W * Y;
else
Vy = W * ((2 * floor(Y / rectangles_y) + 1) * rectangles_y - Y);
(42) Arch
ang = random * W * PI;
Vx = W * sin(ang);
Vy = W * sin(ang)*sin(ang)/cos(ang);
(43) Tangent
Vx = W * sin(X)/cos(Y);
Vy = W * sin(Y)/cos(Y);
(44) Square
Vx = W * (random - 0.5);
Vy = W * (random - 0.5);
(45) Rays
ang = W * random * PI;
r = W / ( X^2 + Y^2 + EPS);
tanr = W * tan(ang) * r;
Vx = tanr * cos(X);
Vy = tanr * sin(Y);
(46) Blade
r = W * random * sqrt(X^2 + Y^2);
Vx = W * X * ( cos(r) + sin(r) );
Vy = W * X * ( cos(r) - sin(r) );
(47) Secant2
r = W * sqrt(X^2 + Y^2);
Vx = W * X;
if (cos(r)<0)
Vy = W * (1.0/cos(r) + 1);
else
Vy = W * (1.0/cos(r) - 1);
(48) Twintrian
r = W * random * sqrt(X^2 + Y^2);
sinr = sin(r);
cosr = cos(r);
diff = log10(sinr*sinr) + cosr;
Vx = W * X * diff;
Vy = W * X * (diff - sinr*PI);
(49) Cross
s = X^2-Y^2;
r = W * sqrt(1.0 / (s^2+EPS));
Vx = X * r;
Vy = Y * r;
(50) Disc2 (parameters: disc2_rot, disc2_twist)
d2rtp = disc2_rot * PI;
disc2_sinadd = sin(disc2_twist);
disc2_cosadd = cos(disc2_twist);
if (disc2_twist > 2*PI) {
k = 1 + disc2_twist - 2*PI;
disc2_sinadd *= k;
disc2_cosadd *= k;
}
if (disc2_twist < -2 * PI) {
k = 1 + disc2_twist + 2*PI;
disc2_sinadd *= k;
disc2_cosadd *= k;
}
t = disc2_rot * PI * (X + Y);
sinr = sin(t);
cosr = cos(t);
r = W * arctan2(X,Y) / PI;
Vx = (sinr + disc2_cosadd) * r;
Vy = (cosr + disc2_sinadd) * r;
(51) Super_Shape (parameters: supershape_m, supershape_n1, supershape_n2, supershape_n3, supershape_holes, supershape_rnd)
pm_4 = supershape_m / 4.0;
pneg1_n1 = -1.0 / supershape_n1;
theta = pm_4 * arctan2(Y,X) + PI/4.0;
t1 = | sin(theta) |;
t2 = | cos(theta) |;
t1 = t1 ^ supershape_n2;
t2 = t2 ^ supershape_n3;
rnd = supershape_rnd;
r = W * ( (rnd*random + (1.0-rnd)*sqrt(X^2+Y^2) - supershape_holes) * (t1+t2)^pneg1_n1 ) / sqrt(X^2+Y^2);
Vx = r * X;
Yy = r * Y;
(52) Flower (parameters: flower_holes, flower_petals)
theta = arctan2(Y,X);
r = W * (random - flower_holes) * cos(flower_petals * theta);
Vx = r * cos(theta);
Vy = r * sin(theta);
(53) Conic (parameters: conic_holes, conic_eccen)
theta = arctan2(Y,X);
r = W * (random - conic_holes) * conic_eccen / (1 + conic_eccen * cos(theta));
Vx = r * cos(theta);
Vy = r * sin(theta);
(54) Parabola (parameters: parabola_height, parabola_width)
r = sqrt(X^2 + Y^2);
Vx = W * parabola_height * sin(r) * sin(r) * random;
Vy = W * parabola_width * cos(r) * random;
(55) Bent2 (parameters: bent2_x, bent2_y)
if (X < 0) X *= bent2_x;
if (Y < 0) Y *= bent2_y;
Vx = W * X;
Vy = W * Y;