Random RGB Color

Generates a random rgb color value to be used by color();

function rndc() = rands(0, 1, 3) ;
 

Radius Of An Arc By Chord And Height

function Radius_Of_An_Arc_By_Chord_And_Height(C,h)=h/2+(C*C)/(8*h);

Related: Circle defined by three points (2d) 

Area Of A Circle Segment By Angle

 function Area_Of_A_Circle_Segment_By_Angle(r,c)=

(r*r)/2*(PI/180*c-sin(c));
 

Area Of A Circle Segment By Height

function Area_Of_A_Circle_Segment_By_Height(r,h)=
    (r*r)*acos((r-h)/r)*((2*PI)/360)-(r-h)*sqrt((2*r*h)-(h*h));
 

Arc Length By Angle

function Arc_Length_By_Angle(radius,central_angle)=

2*PI*radius*(central_angle/360);
 

Area Circle Sector By Arc Length

function Area_Circle_Sector_By_Arc_Length(radius,length)=

(radius*length)/2;

 

Perimeter Of A Circle Sector By Angle

function Perimeter_Of_A_Circle_Sector_By_Angle (radius,central_angle)=

central_angle<360?
2*PI*radius*(central_angle/360)+(2*r)
:2*PI*radius*(central_angle/360);


 

Area Of A Circle Sector By Angle

function Area_Circle_Sector_By_Angle(radius,central_angle)=
       PI*radius*radius*(central_angle/360);

Radius A Regular Polygon By Inradius And N

function Radius_A_Regular_Polygon_By_Inradius_And_N(r,N)=r/(cos/(180/N));

 

List Lerp

Linear interpolation over the items in a list

list=[[1,6],[3,5],[5,3],[1,2],[0,6]];

for(x=[0.01:0.05:4]){
echo(listlerp (list,x));
translate(listlerp (list,x))sphere(0.1);}

function listlerp (l,I)=let(

f=len(l)-1,start=max(0,min(f,floor(I))),

end=max(0,min(f,ceil(I))),bias=I%1) 

(l[end]* bias + l[start] * (1 - bias));

Radius Of Equilateral Triangle By Side

function Radius_Of_Equilateral_Triangle_By_Side (A)=A/(2*sin/(180/3));


 

Volume Of A Pyramid By Sides And Height

function Volume_Of_A_Pyramid_By_Sides_And_Height(A,B,h )= 
    A*B*h*(1/3);
 

Volume Of A Cylinder By Radius And Height

function Volume_Of_A_Cylinder_By_Radius_And_Height(r,h )= 
    PI*r*r*h;
 

Volume Of A Ellipsoid By Radius

function Volume_Of_A_Ellipsoid_By_Radius(r1,r2,r1 )=
    (4/3)*Pi* r1* r2* r3 ;
 

Volume Of A Sphere By Radius

function Volume_Of_A_Sphere_By_Radius(r )=(4/3)*PI* r*r*r ;


 

Mystic Scribbles

Generate a page of random nonsense scribbles in the style of mystic manuscript.

for (rows=[0:20])
{My_poly_line=make_points(120- round(rnd(20)));
translate([rnd(20),rows*27])polyline(My_poly_line);
}
module sline(p1, p2 ,width=0.6,s=12) {
if(abs(p1.x-p2.x)>abs(p1.y-p2.y)){
for(i=[-1/s:1/s:1+1/s]) 
line(xlerp(p1,p2,i),xlerp(p1,p2,i+1/s),width);}
else{for(i=[0:1/s:1-1/s]) 
line(ylerp(p1,p2,i),ylerp(p1,p2,i+1/s),width);}}

module line(p1, p2 ,width=0.3) {
 hull() {        
translate(p1) rotate(45)scale([3,0.1]) circle(width);
translate(p2) rotate(45)scale([3,0.1]) circle(width);    }}


module polyline(p) {for(i=[0:max(0,len(p)-2)])
    if(round(rnd(0.53))==0)sline(p[i],p[i+1]);}
function smooth_curve(a) =
let (b = clamp(a))(b * b * (3 - 2 * b));

function clamp(a, b = 0, c = 1) = min(max(a, b), c);
function lerp(start, end, bias) = (end * bias + start * (1 - bias));
function xlerp(start, end, i) =
     [lerp(start.x,end.x,smooth_curve(i)),lerp(start.y,end.y,i)];
function ylerp(start, end, i) =
     [lerp(start.x,end.x,i),lerp(start.y,end.y,smooth_curve(i))];
 
function make_points(j=10,l1=[-30,-10],l2=[30,10])= 
     ([for(i=[1:j])[
rnd(l1.x,l2.x)/4+i*4,
rnd(l1.y,l2.y)]]);
function rnd(a = 1, b = 0, s = []) = 
  s == [] ? 
   (rands(min(a, b), max(   a, b), 1)[0]) 
  : 
   (rands(min(a, b), max(a, b), 1, s)[0])
  ; 

Volume Of A Prism By Base Heights

function Volume_Of_A_Prism_By_Base_Heights(A,h,H)=
    (1/2)*A*h*H;
 

Volume Of A Prism By Sides Height

function Volume_Of_A_Prism_By_Sides_Height(A,B,C,H)=
    let(s=(a+b+c)/2) sqrt(abs(s*(s-a)*(s-b)*(s-c)))*H;
 

Area Of A Regular Polygon By Inradius And N

function Area_Of_A_Regular_Polygon_By_Inradius_And_N(r,N)= 
    r*r*N*tan(180/n);
 

Area Of A Equilateral Prism By Side Height

function Area_Of_A_Equilateral_Prism_By_Side_Height(A,H)=
    sqrt(3)/4 *(A*A) +A*H*3;
 

Area Of A Prism By Sides Height

function Area_Of_A_Prism_By_Sides_Height(A,B,C,H)=let(s=(a+b+c)/2) 
    2*sqrt(abs(s*(s-a)*(s-b)*(s-c)))+A*H+B*H+C*H;
 

Area Of A Pyramid By Sides And Height

function Area_Of_A_Pyramid_By_Sides_And_Height(A,B,h )= 
    A*B+ 2*( (1/2)* A* (sqrt(h*h+(B/2)*(B/2))) )
       + 2*( (1/2)* B* (sqrt(h*h+(A/2)*(A/2))) );
 

Area Of A Cone By Radius And Height

function Area_Of_A_Cone_By_Radius_And_Height(r,h )= 
    PI*r*r+ PI*r*sqrt(r*r+h*h);