/*
 * 3darc produce an incomplete hollow cylinder
 *
 * ray: ray of the cylinder
 * thick: Thickness of the outside
 * start_angle: Start of the pie to remove
 * end_angle: End of the pie to remove
 */
module 3darc_sub(ray,len,angle){
    if (angle > 90){
        cube([ray,ray,len]);
        rotate([0,0,90]) 3darc_sub(ray,len,angle-90);
    }else{
        intersection(){
            cube([ray,ray,len]);
            rotate([0,0,angle-90]) cube([ray,ray,len]);
        }
    }
}
module 3darc(ray,thick,len,start_angle,end_angle,precision){
    rotate([0,0,end_angle]){
        difference(){
            cylinder(r=ray,h=len,$fn=precision);
            union(){
                if (thick<ray) cylinder(r=ray-thick,h=len,$fn=precision);
                3darc_sub(ray,len,start_angle+360-end_angle);
            }
        }
    }
}

// rectangle with round corner. It is a 2D extruded rectangle
module round_rectangle (width,height,len,radius){
	r2=radius*2;
	// First we create a cross
	translate([radius,0,0]) cube([width-r2,height,len]);
	translate([0,radius,0]) cube([width,height-r2,len]);
	// Then we fill the corners with a cylinder
	translate([radius,radius,0]) rotate([0,0,0]) cylinder(r=radius,h=len,$fn=20);
	translate([width-radius,radius,0]) rotate([0,0,0]) cylinder(r=radius,h=len,$fn=20);
	translate([width-radius,height-radius,0]) rotate([0,0,0]) cylinder(r=radius,h=len,$fn=20);
	translate([radius,height-radius,0]) rotate([0,0,0]) cylinder(r=radius,h=len,$fn=20);
}

// Half cylinder, full
module half_cylinder(ray,len,precision,quarter){
	if (quarter == 1){
		3darc(ray,ray,len,0,180,precision);
	}else if (quarter == 2){
		3darc(ray,ray,len,90,270,precision);
	}else if (quarter == 3){
		3darc(ray,ray,len,180,360,precision);
	}else{
		3darc(ray,ray,len,270,360+90,precision);
	}
}
// Quarter cylinder, full
module quarter_cylinder(ray,len,precision,quarter){
	if (quarter == 1){
		3darc(ray,ray,len,0,90,precision);
	}else if (quarter == 2){
		3darc(ray,ray,len,90,180,precision);
	}else if (quarter == 3){
		3darc(ray,ray,len,180,270,precision);
	}else{
		3darc(ray,ray,len,270,360,precision);
	}
}
// Create a quarter round where the cylinder is removed from a cube
module quarter_concave(ray,len,precision,quarter){
	if (quarter == 1){
		difference(){
			translate([-ray,-ray,0]) cube([ray,ray,len]);
			translate([-ray,-ray,-1]) cylinder(r=ray,h=len+2);
		}
	}else if (quarter == 2){
		difference(){
			translate([0,-ray,0]) cube([ray,ray,len]);
			translate([ray,-ray,-1]) cylinder(r=ray,h=len+2);
		}
	}else if (quarter == 3){
		difference(){
			cube([ray,ray,len]);
			translate([ray,ray,-1]) cylinder(r=ray,h=len+2);
		}
	}else{
		difference(){
			translate([-ray,0,0]) cube([ray,ray,len]);
			translate([-ray,ray,-1]) cylinder(r=ray,h=len+2);
		}
	}
}

// Create an isocel triangle centered on the X axis
module triangle_isocel(width,len,thick){
	linear_extrude(thick){
		polygon([[0,0],[-width/2,0],[0,len],[width/2,0]]);
	}
}
// Create a rectangle triangle
module triangle_rectangle(lenx,leny,thick){
	linear_extrude(thick){
		polygon([[0,0],[lenx,0],[0,leny],[0,0]]);
	}
}
	
		

// Use a 2D path and extrude it along the Z axis
// path=[[x1,y1],[x2,y2],...
// path does not have to be closed
// width is the length along the Z axis
// thick is the thickness. The extrusion will be centered around the path
// offy is normally 0. It is applied to offset from the center of the path
//      for example, if offy=-thick, then the extrusion will be inside the path
// thickr is the ray of the small cylinder used to connect the rectangle joining
//      the points along the path
module profile(path,width,thick,offy,thickr){
    end=len(path)-2;
    for (i=[0:end]){
        x1=path[i][0];
        y1=path[i][1];
        x2=path[i+1][0];
        y2=path[i+1][1];
        diffx = x2-x1;
        diffy = y2-y1;
        angle = atan2(diffy,diffx);
        len = sqrt(diffx*diffx+diffy*diffy);
        translate([x1,0,y1]) rotate([0,-angle,0]){
            translate([0,0,offy-thick/2]) cube([len,width,thick]);
            if (i>0) rotate([-90,0,0]) translate([0,0,0]) cylinder(r=thickr,h=width);
        }
    }
}
// Use a 2D path made of line and arc and extrude it along the Z axis
// path=[[x1,y1,r1],[x2,y2,r2],...
// width is the length along the Z axis
// thick is the thickness. The extrusion will be centered around the path
// offy is normally 0. It is applied to offset from the center of the path
//      for example, if offy=-thick, then the extrusion will be inside the path
		        //cylinder(r=r1,h=width);
// thickr is the ray of the small cylinder used to connect the rectangle joining
//      the points along the path
module profile_arc(path,width,thick,offy,thickr,precision){
    end=len(path)-2;
    for (i=[0:end]){
        x1=path[i][0];
        y1=path[i][1];
	r1=path[i][2];
        x2=path[i+1][0];
        y2=path[i+1][1];
        diffx = x2-x1;
        diffy = y2-y1;
        angle = atan2(diffy,diffx);
        len = sqrt(diffx*diffx+diffy*diffy);
        translate([x1,0,y1]) rotate([0,-angle,0]){
	    if (r1==0){
                translate([0,0,offy-thick/2]) cube([len,width,thick]);
	    }else{
		// We find the half of the angle between the arc center and the two points
		// (The half angle is the angle of a triangle rectangle going between the
		// first point, the arc center and the middle between the two points.
	        sina=(len/2)/r1;
	        angle2=asin(sina);
	        len2=cos(angle2)*r1;
	        translate([len/2,0,0]){
		    //sphere(r=1);
		    rotate([0,90,0]) translate([len2,0,0]){
		        //sphere(r=1);
		        rotate([-90,0,0]) 3darc(r1+thick/2+offy,thick,width,-angle2+180,angle2+180,precision);
	            }
	        }
	    }
            if (i>0) rotate([-90,0,0]) translate([0,0,0]) cylinder(r=thickr,h=width);
	}
    }
}
// Create a rectangle using 3 points
module profile2_plate(x1_1,y1_1,x1_2,y1_2,x2_1,y2_1,width,thick){
        diffx1 = x1_2-x1_1;
        diffy1 = y1_2-y1_1;
        angle1 = atan2(diffy1,diffx1);
        len1 = sqrt(diffx1*diffx1+diffy1*diffy1);

        diffx2 = x2_1-x1_1;
        angle2 = atan2(width,diffx2);
        len2 = sqrt(diffx2*diffx2+width*width);

        diffy3 = y2_1-y1_1;
        angle3 = atan2(diffy3,width);
	translate([0,0,len1/2]) rotate([0,-angle1,0]) triangle(len1,len2,thick);
}
	// Normal vector
module normal(p1,p2,p3){
        diff1_x = p2[0] - p1[0];
        diff1_y = p2[1] - p1[1];
	diff1_z = p2[2] - p1[2];

	diff2_x = p3[0] - p1[0];
	diff2_y = p3[1] - p1[1];
	diff2_z = p3[2] - p1[2];

	a = diff1_y*diff2_z - diff1_z*diff2_y;
	b = diff1_z*diff2_x - diff1_x*diff2_z;
	c = diff1_x*diff2_y - diff1_y*diff2_x;
	echo ("a=",a,"b=",b,"c=",c);
}
// Create a triangle using 3 3d points and a thickness
module profile2_triangle(p1,p2,p3,thick,corra,corrb){
	// Compute the length and angle between p2 and p1
        diff1_x = p2[0] - p1[0];
        diff1_y = p2[1] - p1[1];
	diff1_z = p2[2] - p1[2];

        angle1_y = atan2(diff1_z,diff1_y);
        len1 = sqrt(diff1_x*diff1_x+diff1_y*diff1_y+diff1_z*diff1_z);

        angle1_z = atan2(diff1_x,diff1_y);


	echo ("p2-p1: diff1_x",diff1_x,"diff1_y",diff1_y,"diff1_z",diff1_z,"angle1_y=",angle1_y," angle1_z=",angle1_z);

	// Now do the same between p3 and p1
	diff2_x = p3[0] - p1[0];
	diff2_y = p3[1] - p1[1];
	diff2_z = p3[2] - p1[2];

	angle2_y = atan2(diff2_x,diff2_z);
	len2 = sqrt(diff2_x*diff2_x+diff2_y*diff2_y+diff2_z*diff2_z);

	angle2_z = atan2(diff2_y,diff2_z);

	// Then p3 and p2
	diff3_x = p3[0] - p2[0];
	diff3_y = p3[1] - p2[1];
	diff3_z = p3[2] - p2[2];

	len3 = sqrt(diff3_x*diff3_x+diff3_y*diff3_y+diff3_z*diff3_z);

	cosa = (len3*len3-len1*len1-len2*len2)/(-2*len1*len2);
	angle = acos(cosa);
	
	offx = cosa*len2;
	offy = sin(angle)*len2;
	echo ("len1=",len1,"len2=",len2,"len3=",len3,"offx=",offx,"offy=",offy);
	echo ("p3-p1: diff2_x",diff2_x,"diff2_y",diff2_y,"diff2_z",diff2_z,"angle2_y=",angle2_y," angle2_z=",angle2_z);



	translate([p1[0],p1[1],p1[2]]){
		rotate([-90+angle1_y,0,corrb-angle1_z]){
			cylinder(r=1,h=len1);
		}
		rotate([90+corra,-angle1_y,90+corrb-angle1_z]){
			rotate([angle2_y,0,0]){
				*rotate([-90,0,0]) cylinder(r=1,h=offy);
				translate([0,0,-0.5]) linear_extrude(1){
					polygon([[0,0],[len1,0],[offx,offy],[0,0]]);
				}
			}
		}
	}
}
module profile2_sphere(p){
	translate([p[0],p[1],p[2]]) sphere (r=1);
}

// Use 2 2D path and extrude from one to the other
module profile2(path1,path2,width,thick,offy,thickr){

    normal ([1,2,3],[4,6,9],[12,11,9]);
    end=len(path1)-2;
    pt=1;
    for (i=[0:end]){
    //for (i=[0:end]){
        p1=[path1[i][0],0,path1[i][1]];
        p2=[path2[i][0],width,path2[i][1]];
        p3=[path2[i+1][0],width,path2[i+1][1]];
        p4=[path1[i+1][0],0,path1[i+1][1]];

	profile2_triangle (p1,p2,p4,thick,0,0);
	//profile2_triangle (p2,p4,p3,thick,90,180);

	profile2_sphere (p1);
	profile2_sphere (p2);
	profile2_sphere (p3);
	profile2_sphere (p4);
    }
}
// Draw an hexagonal screw nut
// The size is the distance between two opposite parallel side
// The depth is the thickness of the nut
// flat is a boolean. The nut is drawn either with a peak at the top of flat line
module nut(size,depth,flat){
	rotate([0,0,flat ? 30 : 0]){
		linear_extrude(depth){
			basex=size/2;
			s2=basex/cos(30);
			x=sin(30)*s2;
			polygon([[-basex,0],[-basex,-x],[0,-s2],[basex,-x],
				[basex,x],[0,s2],[-basex,x],[-basex,0]]);
		}
	}
}

module donut(ray,thick,precision){
	rotate_extrude($fn=precision){
		translate([ray,0,0]) circle(r=thick/2);
	}
}