// ======================================================================
// CORES E TEXTURAS

background { color rgb < 1,1,1 > }

#declare tx_esfera =
	texture {
	    pigment { color rgb < 1,0,1 > }
		finish{ diffuse 1 }
    }


// ======================================================================
// DESCRIÇÃO DA CENA 

// Partes da cena

#include "eixos.inc"

#macro linearInterpolation(t0,v0, t1,v1, tt)
	#local r = (tt-t0)/(t1-t0);
	#local s = 1 - r;
	#local vv = s*v0 + r*v1;
	vv
#end

#macro bezierCurve(t0,t1, A,B,C,D, tt)
	#local AB = linearInterpolation(t0,A, t1,B, tt);
	#local BC = linearInterpolation(t0,B, t1,C, tt);
	#local CD = linearInterpolation(t0,C, t1,D, tt);
	#local ABC = linearInterpolation(t0,AB, t1,BC, tt);
	#local BCD = linearInterpolation(t0,BC, t1,CD, tt);
	#local ABCD = linearInterpolation(t0,ABC, t1,BCD, tt);
	ABCD
#end

#macro smoothenCurves(P, n, i)
    #local j = mod(i+1,n);
    #local vv = (P[j][1]-P[i][2])/2;
    #local P[i][2] = P[i][3]-vv;
    #local P[j][1] = P[j][0]+vv;
#end

#macro drawBezier(A,B,C,D)
    #for (i, 0, 1, 0.001)
        object { esfera translate bezierCurve(0,1, A,B,C,D, i) }
    #end
#end

#macro drawCurve()
    #local P = array[3][4] {
        {<0.3,-0.5,1>, <-1,0.5,0.66>, <-1,0.5,0.33>, <0.8,0,0>},
        {<0.8,0,0>, <0.66,0.5,0.5>, <0.33,-1,0.9>, <0.3,0,0.5>},
        {<0.3,0,0.5>, <0,0.8,-0.8>, <-0.5,-1,-1>, <0.3,-0.5,1>}
    };
    
    #local Q = array[3][4] {
        {<-0.3,-0.5,1>, <-1,0.5,0.66>, <-1,0.5,0.33>, <-0.8,0,0>},
        {<-0.8,0,0>, <0.66,0.5,0.5>, <0.33,-1,0.9>, <-0.3,0,0.5>},
        {<-0.3,0,0.5>, <0,0.8,-0.8>, <-0.5,-1,-1>, <-0.3,-0.5,1>}
    };
    
    #for (i, 0, 2)
        smoothenCurves(P, 3, i)
        smoothenCurves(Q, 3, i)
    #end
    
    #local R = array[2][3][4];
    
    #for (i, 0, 1, 0.01)
        #local R = matrixInterpolation(R,0,1,2, 0,1,i);
    #end
    
    #for (i, 0, 2)
        smoothenCurves(R, 3, i)
    #end
    
    
	union {
		drawBezier(R[0][0], R[0][1], R[0][2], R[0][3])
		drawBezier(R[1][0], R[1][1], R[1][2], R[1][3])
		drawBezier(R[2][0], R[2][1], R[2][2], R[2][3])
	}
#end
	
#macro matrixInterpolation(P, k0,k1, NA, t0,t1, tt)
// Interpola P[k0][i][j] e P[k1][i][j] e coloca em R[i][j]
    #local R = array[NA][4];
    
    #for (i, 0, NA-1)
        #for (j, 0, 3)
            #local R[i][j] = linearInterpolation(t0,t1, P[k0][i][j],P[k1][i][j], tt);
        #end
    #end
    
    R
#end

#macro func(i)
    i*i
#end

#declare esfera = sphere {
	< func(clock-0.5), func(clock-0.5)*2, func(clock-0.5)/4 >, 0.2
	texture{ tx_esfera }
}


// Aqui está a cena, finalmente:

object { eixos(1) }

object { esfera }


#include "camlight.inc"
#declare centro_cena = < 0,0,0 >;
#declare raio_cena = 2;
#declare dir_camera = < 90, 90, 90 >; // 0, -1, 90 for XY
#declare dist_camera = 4*raio_cena;
#declare intens_luz = 1.4;
camlight(centro_cena, raio_cena, dir_camera, dist_camera , z, intens_luz)