dotSCAD/examples/turtle/hilbert_dragon.scad

use <along_with.scad>;
use <hull_polyline3d.scad>;
use <bezier_smooth.scad>;
use <ellipse_extrude.scad>;
use <shape_trapezium.scad>;
use <util/reverse.scad>;
use <util/dedup.scad>;
use <turtle/lsystem3.scad>;

hilbert_dragon();

module hilbert_dragon() {
    module scales(ang, leng, radius, height, thickness) {
        module one_scale() {
            rotate([0, ang, 0]) 
            linear_extrude(thickness, center = true) 
            scale([leng, 1]) 
                circle(1, $fn = 4);    
        }

        for(a = [0:45:315]) {
            rotate(a) 
            translate([radius, 0, height]) 
                one_scale();
                
            rotate(a + 15) 
            translate([radius, 0, height + 1.75]) 
                one_scale();
        }
    }

    module one_segment() {
        // scales
        scale([1,0.85,1]) union() {
            scales(60, 4, 5, 0, 1.5);
            scales(75, 2.5, 5, -4, 1.25);
            scales(100, 1.25, 4.5, -7, 1);
            scales(110, 1.25, 3, -9, 1);
            scales(120, 2.5, 2, -9, 1);   
        }
        
        // hair
        for(i = [0:1]) {
            rotate([15 -15 * i, 0, 0]) 
            translate([0, 3, -4]) 
            rotate([45, 90, 0]) 
            linear_extrude(2, center = true) 
            scale([2, 2, 1]) 
                circle(2.5, $fn = 3);
        }                

        // belly
        translate([0, -3, 1]) 
        rotate([-10, 0, 0]) 
        scale([1.1, 0.8, 1.25])  
            sphere(5.5, $fn = 8); 
            
    }

    module head(angy_angz) {
        module hair() {
            for(i = [18:35]) {
                rotate(i * 10) 
                translate([0, -14, 0]) 
                rotate([9, 0, 0]) 
                linear_extrude(15, scale = 0, twist = 30) 
                translate([0, 10, 0]) 
                    circle(3, $fn = 3);    
            }       

            for(i = [0:35]) {
                rotate(i * 10) 
                translate([0, -12, 0]) 
                rotate([5, 0, 0]) 
                linear_extrude(20, scale = 0, twist = 30) 
                translate([0, 10, 0]) 
                    circle(2, $fn = 3);    
            }
            
            for(i = [0:35]) {
                rotate(i * 10) 
                translate([0, -10, 0]) 
                rotate([2, 0, 0]) 
                linear_extrude(22, scale = 0, twist = -30) 
                translate([0, 10, 0]) 
                    circle(3, $fn = 3);    
            }     
        }
        
        module one_horn() {        
            translate([-10, -4, -1]) 
            rotate([40, -25, 0]) 
            linear_extrude(30, scale = 0, twist = -90) 
            translate([7.5, 0, 0]) 
                circle(3, $fn = 4);    
        }
        
        module mouth() {
            translate([0, 0, -2]) 
            rotate([90, 0, -90]) 
            ellipse_extrude(8, slices = 2) 
                polygon(
                    shape_trapezium([4, 15], 
                    h = 22,
                    corner_r = 0)
                );       
            
            translate([0, 0, -3]) 
            rotate([90, 0, -90]) 
             ellipse_extrude(6, slices = 4) 
                 polygon(
                    shape_trapezium([6, 20], 
                    h = 20,
                    corner_r = 0)
                );    
                        
            mirror([1, 0, 0]) 
            translate([0, 0, -3]) 
            rotate([85, 0, -90])
            ellipse_extrude(4, slices = 2) 
                polygon(
                    shape_trapezium([6, 19], 
                    h = 20,
                    corner_r = 0)
                );       
        }
        
        module one_eye() {
            translate([-5, 3, -2]) 
            rotate([-15, 0, 75]) 
            scale([1, 1, 1.5]) 
                sphere(1.5, $fn = 5);      

            translate([-5.5, 3.5, -2.5]) 
            rotate([-15, 0, 75]) 
                sphere(0.5, $fn = 12);                      
        }
        
        module one_beard() {
            translate([-11, -12, -11])
            rotate(180) 
            linear_extrude(10, scale = 0, twist = 90) 
            translate([-10, -10, 0]) 
                circle(0.75, $fn = 6);    
        }
        


        rotate([0, angy_angz[0] + 15, angy_angz[1]]) 
        translate([0, 0, -25 / 2]) 
        scale(1.15) {
           scale([0.8, 0.9, 1]) hair();

            translate([0, 0, 2]) {
                rotate(-90) {
                     one_horn();
                     mirror([-1, 0, 0]) one_horn();       
                }
                
                mouth();

                one_eye();
                mirror([0, 1, 0]) one_eye();
                
                one_beard();
                mirror([0, 1, 0]) one_beard();
            }        
        }
    }

    lines = hilbert_curve();
    hilbert_path = dedup(
        concat(
            [for(line = lines) line[0]], 
            [lines[len(lines) - 1][1]])
        );
    smoothed_hilbert_path = bezier_smooth(hilbert_path, 0.45, t_step = 0.2);

    dragon_body_path = reverse([for(i = [1:len(smoothed_hilbert_path) - 2]) smoothed_hilbert_path[i]]);
     
    along_with(dragon_body_path, scale = 0.6)    
    rotate([90, 0, 0]) 
    scale(0.04)  
        one_segment();

    translate([0, 0, -2.5])        
    scale(0.035)         
        head([0, 0]);     
}
   

function hilbert_curve() = 
    let(
        axiom = "A",
        rules = [
            ["A", "B-F+CFC+F-D&F^D-F+&&CFC+F+B//"],
            ["B", "A&F^CFB^F^D^^-F-D^|F^B|FC^F^A//"],
            ["C", "|D^|F^B-F+C^F^A&&FA&F^C+F+B^F^D//"],
            ["D", "|CFB-F+B|FA&F^A&&FB-F+B|FC//"]
        ]
    )
    lsystem3(axiom, rules, 2, 90, 1, 0,  [0, 0, 0]);