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Rounded Cube and Face Triangulation #4

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dd02e97
Added a heavy roundedcube 'primitive' and added a face triangulation
Jan 30, 2018
53a743c
Polygon face triangulation
Jan 30, 2018
1ea16d0
Add roundedcube.scad for rounded cube.
Jan 30, 2018
92a32a4
roundedcube out again
Jan 30, 2018
a477917
roundedcube out again
Jan 30, 2018
bee54b6
roundedcube back in
Jan 30, 2018
a934d61
Update subdivision.scad
NateTG Feb 20, 2018
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148 changes: 148 additions & 0 deletions roundedcube.scad
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Original file line number Diff line number Diff line change
@@ -0,0 +1,148 @@
use<functional.scad>

/* Rounded cube using the cube/octahedron duality. */

function rounded_cube(size, r=0, center=false, fn=12)=
(!is_array(size))?
rounded_cube(size=[size,size,size],r=r,center=center,fn=fn)
:(r>=min(size[0],size[1],size[2])/2)?
rounded_cube(size=size,r=min(size[0],size[1],size[2])/2-.0001,center=center,fn=fn)
:(r<=0)?
cube(size,center=center)
:
let(
steps=(fn>0)?ceil(fn/4):1,
sx=size[0]/2-r,
sy=size[1]/2-r,
sz=size[2]/2-r,
da=90/steps,
count=4*(steps+1)*(steps+2)-1,
rcube=[
flatten(concat(
[for (i=[0:steps])
let(
z=r*(-cos(da*i))-sz,
l=r*sin(da*i),
dp=(i>0)?(90/i):0
)
concat(
[for(j=[0:i]) [sx+l*cos(dp*j),sy+l*sin(dp*j),z]],
[for(j=[0:i]) [-sx-l*sin(dp*j),sy+l*cos(dp*j),z]],
[for(j=[0:i]) [-sx-l*cos(dp*j),-sy-l*sin(dp*j),z]],
[for(j=[0:i]) [sx+l*sin(dp*j),-sy-l*cos(dp*j),z]]
)
],
[for (i=[steps:-1:0])
let(
z=sz+r*cos(da*i),
l=r*sin(da*i),
dp=(i>0)?90/i:0
)
concat(
[for(j=[0:i]) [sx+l*cos(dp*j),sy+l*sin(dp*j),z]],
[for(j=[0:i]) [-sx-l*sin(dp*j),sy+l*cos(dp*j),z]],
[for(j=[0:i]) [-sx-l*cos(dp*j),-sy-l*sin(dp*j),z]],
[for(j=[0:i]) [sx+l*sin(dp*j),-sy-l*cos(dp*j),z]]
)
]
)),
//Each side on the i'th row has i+1 points
//The rows start with 0,4,8,12 ... 2*i*(i+1)
//Each side on the ith row has i+1 points
concat(
[[0,1,2,3]],
[for(i=[1:steps]) let(start=2*i*(i+1),laststart=2*i*(i-1),
ppl=4*(i+1),lppl=4*i,
pps=(i+1),lpps=i
)
for(side=[0:3])
[
laststart+lpps*side,
laststart+(lpps*side+lppl-1)%lppl,
start+(pps*side+ppl-1)%ppl,
start+pps*side
]
],
[for(i=[1:steps]) let(start=2*i*(i+1),laststart=2*i*(i-1),
ppl=4*(i+1),lppl=4*i,
pps=(i+1),lpps=i
)
for(side=[0:3]) for(j=[0:i-1])
[
laststart+lpps*side+j,
start+pps*side+j,
start+pps*side+1+j
]
],
(steps<2)?[]: [for(i=[2:steps]) let(start=2*i*(i+1),laststart=2*i*(i-1),
ppl=4*(i+1),lppl=4*i,
pps=(i+1),lpps=i
)
for(side=[0:3]) for(j=[0:i-2])
[
laststart+lpps*side+j,
start+pps*side+j+1,
laststart+lpps*side+j+1
]
],
//These faces fuse the top & bottom
//The steps'th row starts with 2*steps*(steps+1)
//The (steps+1)'th row starts with 2*steps*(steps+1)+4*steps
[for(side=[0:3]) let(start=2*steps*(steps+1)+4*(steps+1),
laststart=2*steps*(steps+1),
ppl=4*(steps+1),lppl=4*(steps+1),
pps=(steps+1),lpps=(steps+1)
) for(j=[0:steps])

[
laststart+lpps*side+j,
laststart+(lpps*side+lppl-1+j)%lppl,
start+(pps*side+ppl-1+j)%ppl,
start+pps*side+j
]
],
//And the top is just the bottom wound in reverse.
[[count-0,count-1,count-2,count-3]],
[for(i=[1:steps]) let(start=2*i*(i+1),laststart=2*i*(i-1),
ppl=4*(i+1),lppl=4*i,
pps=(i+1),lpps=i
)
for(side=[0:3])
[
count-(laststart+lpps*side),
count-(laststart+(lpps*side+lppl-1)%lppl),
count-(start+(pps*side+ppl-1)%ppl),
count-(start+pps*side)
]
],
[for(i=[1:steps]) let(start=2*i*(i+1),laststart=2*i*(i-1),
ppl=4*(i+1),lppl=4*i,
pps=(i+1),lpps=i
)
for(side=[0:3]) for(j=[0:i-1])
[
count-(laststart+lpps*side+j),
count-(start+pps*side+j),
count-(start+pps*side+1+j)
]
],
(steps<2)?[]: [for(i=[2:steps]) let(start=2*i*(i+1),laststart=2*i*(i-1),
ppl=4*(i+1),lppl=4*i,
pps=(i+1),lpps=i
)
for(side=[0:3]) for(j=[0:i-2])
[
count-(laststart+lpps*side+j),
count-(start+pps*side+j+1),
count-(laststart+lpps*side+j+1)
]
]
)
]
)
center?rcube:translate(size/2,rcube)
;

rcube=(rounded_cube([3,2,1],1/3,fn=24,center=false));
poly3d(rcube);

120 changes: 120 additions & 0 deletions subdivision.scad
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
use <functional.scad>

// faces better be triangles... or else!

function subdivide_faces(n=1, poly) =
let(
points = poly[0],
Expand Down Expand Up @@ -28,3 +29,122 @@ function subdivide_faces(n=1, poly) =
])
)
n > 1 ? subdivide_faces(n-1, [allpoints, faces]) : n > 0 ? [allpoints,faces] : poly;

//Utility function for splitting circular vectors.
function circle_cut (list,start,end)=
(end<start)?
concat([for (i=[start:len(list)-1]) list[i]],[for (i=[0:end]) list[i]])
:
[for (i=[start:end]) list[i]]
;

//Ineffictient (Order N^2) naive face triangulation function that works
//by ear clipping:
//Finds a convex vertex (order N)
//Checks if the 'ear' with that vertex contains any points.
//If not, the ear can be clipped, otherwise there's a diagonal in the ear,

function triangulate_poly3d(poly)=
[poly[0],triangulate_faces(poly[0],poly[1])]
;

function triangulate_faces(points,faces)=
flatten([for(i=[0:len(faces)-1]) triangulate_face(points,faces[i])])
;

function triangulate_face(points,face)=
let(count=len(face))
(3==count)?
[face]
:
let(wd=face_winding(points,face),cv=convex_vertex(wd,points,face),
pv=(count+cv-1)%count,nv=(cv+1)%count,
p0=points[face[pv]],p1=points[face[cv]],p2=points[face[nv]],
tests=[
[cross(wd,p0-p2),cross(wd,p0-p2)*p0],
[cross(wd,p1-p0),cross(wd,p1-p0)*p1],
[cross(wd,p2-p1),cross(wd,p2-p1)*p2]
],
eartest=point_in_ear(points,face,tests),
clipableear=(eartest[0]<0),
diagonalpoint=eartest[1]
)
(clipableear)? //There is no point inside the ear.
flatten([
[circle_cut(face,pv,nv)],
triangulate_face(points,circle_cut(face,nv,pv))
])
: //If there is a point inside the ear, make a diagonal and clip along that.
flatten([
triangulate_face(points,circle_cut(face,cv,diagonalpoint)),
triangulate_face(points,circle_cut(face,diagonalpoint,cv))
])
;

function vsum(v_list,i=0)=
(i<len(v_list)-1)?
v_list[i]+vsum(v_list,i+1)
:
[0,0,0]
;

function face_winding(points,face)=
let(count=len(face))
vsum([
for(i=[0:count-3]) cross(
points[face[(i+1)]]-points[face[0]],
points[face[(i+2)]]-points[face[(i+1)]]
)
])
;

function convex_vertex(wd,points,face,i=0)=
let(count=len(face),
p0=points[face[i]],p1=points[face[(i+1)%count]],p2=points[face[(i+2)%count]]
)
(len(face)>i)?
(cross(p1-p0,p2-p1)*wd>0)?
(i+1)%count
:
convex_vertex(wd,points,face,i+1)
://This should never happen since there is at least 1 convex vertex.
undef
;

//The order of tests matters - This assumes Test 0 indicates which point is furthest in
//the ear - and that point will form a diagonal with the tip of the ear.

function point_in_ear(points,face,tests,i=0)=
(i<len(face)-1)?
let(
prev=point_in_ear(points,face,tests,i+1),
test=check_point_in_ear(points[face[i]],tests)
)
(test>prev[0])?
[test,i]
:
prev
:
[check_point_in_ear(points[face[i]],tests),i]
;

function check_point_in_ear (point,tests)=
let(
result=[
(point*tests[0][0])-tests[0][1],
(point*tests[1][0])-tests[1][1],
(point*tests[2][0])-tests[2][1]
]
)
(result[0]>0 && result[1]>0 && result[2]>0)?
result[0]
:
-1
;