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#info fold and cut regular polyhedra Distance Estimator (knighty 2012)
#define providesInit
#define providesColor
#include "DE-Raytracer.frag"
#include "MathUtils.frag"

#group polyhedra

// Symmetry group type.
uniform int Type;  slider[3,5,5]

// U 'barycentric' coordinate for the 'principal' node
uniform float U; slider[0,1,1]

// V
uniform float V; slider[0,0,1]

// W
uniform float W; slider[0,0,1]

//vertex radius 
uniform float VRadius; slider[0,0.05,0.5]

//segments radius 
uniform float SRadius; slider[0,0.01,0.1]

uniform bool displayFaces; checkbox[true]
uniform bool displaySegments; checkbox[true]
uniform bool displayVertices; checkbox[true]

#group polyhedraColor
uniform vec3 face0Color; color[0.0,0.0,0.0]
uniform vec3 face1Color; color[0.0,0.0,0.0]
uniform vec3 face2Color; color[0.0,0.0,0.0]
uniform vec3 verticesColor; color[0.0,0.0,0.0]
uniform vec3 segmentsColor; color[0.0,0.0,0.0]

#define PI 3.14159
vec3 nc,p,pab,pbc,pca;
void init() {
	float cospin=cos(PI/float(Type)), scospin=sqrt(0.75-cospin*cospin);
	nc=vec3(-0.5,-cospin,scospin);
	pab=vec3(0.,0.,1.);
	pbc=normalize(vec3(scospin,0.,0.5));
	pca=normalize(vec3(0.,scospin,cospin));
	p=normalize((U*pab+V*pbc+W*pca));
}

vec3 fold(vec3 pos) {
	for(int i=0;i<Type;i++){
		pos.xy=abs(pos.xy);
		float t=-2.*min(0.,dot(pos,nc));
		pos+=t*nc;
	}
	return pos;
}

float D2Planes(vec3 pos) {
	float d0=dot(pos,pab)-dot(pab,p);
	float d1=dot(pos,pbc)-dot(pbc,p);
	float d2=dot(pos,pca)-dot(pca,p);
	return max(max(d0,d1),d2);
}

float D2Segments(vec3 pos) {
	pos-=p;
	float dla=length(pos-min(0.,pos.x)*vec3(1.,0.,0.));
	float dlb=length(pos-min(0.,pos.y)*vec3(0.,1.,0.));
	float dlc=length(pos-min(0.,dot(pos,nc))*nc);
	return min(min(dla,dlb),dlc)-SRadius;//max(max(dla,dlb),max(dlc,dlp))-SRadius;
}

float D2Vertices(vec3 pos) {
	return length(pos-p)-VRadius;
}

float DE(vec3 pos) {
	pos=fold(pos);
	float d=10000.;
	if(displayFaces) d=min(d,D2Planes(pos));
	if(displaySegments) d=min(d,D2Segments(pos));
	if(displayVertices) d=min(d,D2Vertices(pos));
	return d;
}

vec3 color(vec3 pos, vec3 normal){
	pos=fold(pos);
	float d0=1000.0,d1=1000.0,d2=1000.,dv=1000.,ds=1000.;
	if(displayFaces){
		d0=abs(dot(pos,pab)-dot(pab,p));
		d1=abs(dot(pos,pbc)-dot(pbc,p));
		d2=abs(dot(pos,pca)-dot(pca,p));
	}
	if(displaySegments) ds=D2Segments(pos);
	if(displayVertices) dv=D2Vertices(pos);
	float d=min(min(d0,min(d1,d2)),min(ds,dv));
	vec3 col=face0Color;
	if(d==d1) col=face1Color;
	if(d==d2) col=face2Color;
	if(d==ds) col=segmentsColor;
	if(d==dv) col=verticesColor;
	return col;
}

#preset default
FOV = 0.62536
Eye = -3.59281,-1.35854,-1.5123
Target = 4.11696,1.54296,1.75405
Up = 0.476591,-0.750108,-0.458475
AntiAlias = 1
Detail = -3
DetailAO = -1.57143
FudgeFactor = 1
MaxRaySteps = 88
BoundingSphere = 2
Dither = 0.4386
NormalBackStep = 1
AO = 0,0,0,0.90123
Specular = 4.4304
SpecularExp = 16
SpotLight = 1,1,1,0.75
SpotLightDir = 0.6923,0.78462
CamLight = 1,0.827451,0.768627,0.6415
CamLightMin = 0
Glow = 1,1,1,0
GlowMax = 20
Fog = 0
HardShadow = 0
ShadowSoft = 8.254
Reflection = 0
BaseColor = 0.721569,0.721569,0.721569
OrbitStrength = 0.37662
X = 0.411765,0.6,0.560784,0.41748
Y = 0.666667,0.666667,0.498039,-0.16504
Z = 1,0.258824,0.207843,1
R = 0.0823529,0.278431,1,0.82352
BackgroundColor = 0.501961,0.737255,0.956863
GradientBackground = 0.86955
CycleColors = true
Cycles = 4.04901
EnableFloor = false
FloorNormal = 0,0,0
FloorHeight = 0
FloorColor = 1,1,1
Type = 5
U = 1
V = 0.54545
W = 0
VRadius = 0.08427
SRadius = 0.02921
displayFaces = true
displaySegments = true
displayVertices = true
face0Color = 0.796078,0.611765,0.172549
face1Color = 0.164706,0.74902,0.12549
face2Color = 0.164706,0.305882,0.764706
verticesColor = 1,0,0
segmentsColor = 0.25098,0.760784,0.490196
#endpreset

// You must call the argument "vp".
int PluginVarPrepare(Variation* vp)
{
    VAR(cx) = -VAR(poincare3D_r) * cos(VAR(poincare3D_a)*M_PI_2) * cos(VAR(poincare3D_b)*M_PI_2);
    VAR(cy) =  VAR(poincare3D_r) * sin(VAR(poincare3D_a)*M_PI_2) * cos(VAR(poincare3D_b)*M_PI_2);
    VAR(cz) = -VAR(poincare3D_r) * sin(VAR(poincare3D_b)*M_PI_2);

    VAR(c2) = sqr(VAR(cx)) + sqr(VAR(cy)) + sqr(VAR(cz));

    VAR(c2x) = 2 * VAR(cx);
    VAR(c2y) = 2 * VAR(cy);
    VAR(c2z) = 2 * VAR(cz);

    VAR(s2x) = sqr(VAR(cx)) - sqr(VAR(cy)) - sqr(VAR(cz)) + 1;
    VAR(s2y) = sqr(VAR(cy)) - sqr(VAR(cx)) - sqr(VAR(cz)) + 1;
    VAR(s2z) = sqr(VAR(cz)) - sqr(VAR(cy)) - sqr(VAR(cx)) + 1;

    // Always return TRUE.
    return TRUE;
}

// You must call the argument "vp".
int PluginVarCalc(Variation* vp)
{
    double r2 = sqr(FTx) + sqr(FTy) + sqr(FTz);

    double x2cx = VAR(c2x)*FTx, y2cy = VAR(c2y)*FTy, z2cz = VAR(c2z)*FTz;

    double d = VVAR / (
        VAR(c2) * r2 - x2cx - y2cy - z2cz + 1
        );

    FPx += d * (
        FTx * VAR(s2x) + VAR(cx) * (y2cy + z2cz - r2 - 1)
    );
    FPy += d * (
        FTy * VAR(s2y) + VAR(cy) * (x2cx + z2cz - r2 - 1)
    );
    FPz += d * (
        FTz * VAR(s2z) + VAR(cz) * (y2cy + x2cx - r2 - 1)
    );

    return TRUE;
}

int PluginVarPrepare(Variation* vp)
{
    double pa = 2*M_PI / VAR(hypertile3D_p),
           qa = 2*M_PI / VAR(hypertile3D_q);

    double r = -(cos(pa) - 1) / (cos(pa) + cos(qa));
    if (r > 0)
        r = 1 / sqrt(1 + r);
    else
        r = 1;

    double na = VAR(hypertile3D_n) * pa;

    VAR(cx) = r * cos(na);
    VAR(cy) = r * sin(na);

    VAR(c2) = sqr(VAR(cx)) + sqr(VAR(cy));

    VAR(c2x) = 2 * VAR(cx);
    VAR(c2y) = 2 * VAR(cy);

    VAR(s2x) = 1 + sqr(VAR(cx)) - sqr(VAR(cy));
    VAR(s2y) = 1 + sqr(VAR(cy)) - sqr(VAR(cx));
    VAR(s2z) = 1 - sqr(VAR(cy)) - sqr(VAR(cx));

    // Always return TRUE.
    return TRUE;
}

// You must call the argument "vp".
int PluginVarCalc(Variation* vp)
{
    double r2 = sqr(FTx) + sqr(FTy) + sqr(FTz);

    double x2cx = VAR(c2x)*FTx,
           y2cy = VAR(c2y)*FTy;

    double d = VVAR / (
        VAR(c2) * r2 + x2cx - y2cy + 1
        );

    FPx += d * (
        FTx * VAR(s2x) - VAR(cx) * ( y2cy - r2 - 1)
    );
    FPy += d * (
        FTy * VAR(s2y) + VAR(cy) * (-x2cx - r2 - 1)
    );
    FPz += d * (
        FTz * VAR(s2z)
    );

    return TRUE;
}