<- previous index next ->
It may take a sequence of files to get the final 3D printer object you want.
This page shows what I used to get a pipe curved into a toroid.
In addition to getting the correct shape of an object, covered in triangles,
the normal vector from every triangle must point out from the object.
The normal vector for the top of the object must point up.
The normal vector for the bottom of the object must point down.
The normal vector for the outside of the object must point out.
The normal vector for the inside, if there is an inside, must point in.
The normal vector to a triangle with points P1, P2, P3 each with x,y,z is:
ax = P3 x - P2 x length from P3 to P2
ay = P3 y - P2 y P1
az = P3 z - P2 z / \ Taking points clockwise
bx = P2 x - P1 x length from P2 to P1 / \ reverses the direction of
by = P2 y - P1 y P3____P2 the normal from counter
bz = P2 z - P1 z clockwise. The code shown
nx = ay*bz-az*by direction of normal is for counter clockwise
ny = az*bx-ax*bz normal points out of screen.
nz = ax*by-ay*bx
s = sqrt(nx*nx+ny*ny+nz*nz) standard to make the length of normal vector 1.0
nx = nx / s final vector normal to triangle
ny = ny / s
nz = nz / s
The code in java, given P1 x in v[0][0], P1 y in v[0][1], P1 z in v[0][2]
P2 in v[1], P3 in v[2] computes the normal vector nx, ny, nz.
ax = v[2][0] - v[1][0];
ay = v[2][1] - v[1][1];
az = v[2][2] - v[1][2];
bx = v[1][0] - v[0][0];
by = v[1][1] - v[0][1];
bz = v[1][2] - v[0][2];
nx = ay*bz-az*by;
ny = az*bx-ax*bz;
nz = ax*by-ay*bx;
s = Math.sqrt(nx*nx+ny*ny+nz*nz);
nx = nx / s;
ny = ny / s;
nz = nz / s;
The code sequence and output is:
Base just inside, outside, top and bottom to get normal in correct direction
cyl1_base.java
cyl1_base.dat
cyl1_base.stl
The code sequence and output to get a short pipe is:
cyl1_pipe.java
cyl1_pipe.dat
cyl1_pipe.stl
The code sequence and output to slope the pipe is:
cyl1_slop.java
cyl1_slop.dat
cyl1_slop.stl
The code sequence and output to curve the pipe 360 degrees,
first try to get inside, outside and just bottom, 8 bends,
and thus just the upper half, make two and glue together, is:
hcyl1_curv8.java
hcyl1_curv8.dat
hcyl1_curv8.stl
rotated 90 degrees to see direction of normal vectors
The code sequence and output for 16 bends, smoother, is:
hcyl1_curv16.java
hcyl1_curv16.dat
hcyl1_curv16.stl
The code sequence and output for 32 bends, smoother is:
hcyl1_curv.java
hcyl1_curv.dat
hcyl1_curv.stl
Having a .stl file, you can compute area and volume of the object:
read_stl.java
volume_stl.java
volume_stl_java.out
bound1a.stl
volume_stl_cube1.out
cube1.stl
<- previous index next ->
Many web sites on Java GUI, AWT, Swing, etc.
Many web sites on Python wx, tk, qt, etc.