How do I create a solid shape that has a smaller area on the bottom surface than the top surface?

My code as of now is:

 [x y] = meshgrid(-1:0.1:1); % Generate x and y data
z = zeros(size(x, 1)); % Generate z data
surf(x, y, z) % Plot the surface

 %finding S value

 xmin=min(min(x));
 xmax=max(max(x));
 ymin=min(min(y));
 ymax=max(max(y));
 zmin=min(min(z));
 zmax=max(max(z));

 SX=xmax-xmin;
 SY=ymax-ymin;
 SZ=2*(zmax-zmin);

 S= largest value between SX, SY, and SZ
 S=2;

 figure(2)
 surf2solid(x,y,x,S,5);

I want my final 3D shape to be tapered such that the area of the bottom surface is smaller than the top surface. I'm trying to get the X plane (on the lowest Z axis) to be smaller than the top surface.

[John D'Errico]

What is surf2solid? MATLAB does not provide that tool. I'll guess this:

https://www.mathworks.com/matlabcentral/fileexchange/42876-surf2solid-make-a-solid-volume-from-a-surface-for-3d-printing

Anyway, what specific shape are you trying to create? A conic frustrum perhaps?

[Rebekah Abrams]

I found surf2solid at this link but its the same thing as your link.The actual shape I want to use tapering for is fairly complex so for simplicity, the shape I am making is generally rectangular. Ideally, I'd want to just taper the longer sides and leave the shorter sides as is.

Answer 1

[John D'Errico]

Hmm. But not hard in any case. Best if the top and bottom polggons are the same length.

Suppose we create two polygons. If they have the same number of nodes, that is best, since then it is just a really simple mapping.

P1x = [0 3 3 0 0];
P1y = [0 0 3 3 0];
np = numel(P1x);

So a square for the base, of side length 3.

The top is a rectangle. 3 units wide on one edge, 1 unit wide on the other.

P2x = [0 3 3 0 0];
P2y = [1 1 2 2 1];

Height? 5 units.

zminmax = [0 5];

Well, that part was easy. Really though, you should follow rule number 1.

Rule number 1: ALWAYS plot EVERYTHING.
Rule number 2: See rule 1.
Rule number 3: Do you really honestly, seriously need to ask what rule number 3 is?

plot3(P1x,P1y,repmat(zminmax(1),1,np),'ro-')
hold on
plot3(P2x,P2y,repmat(zminmax(2),1,np),'bs-')

In fact, we can probably use similar calls to fill in the top and bottom faces of the frustrum, just using fill3.

First though, the sides.

t = linspace(0,1,11)';
X = t*P1x + (1-t)*P2x;
Y = t*P1y + (1-t)*P2y;
Z = t*repmat(zminmax(1),1,np) + (1-t)*repmat(zminmax(2),1,np);
surf(X,Y,Z)

hold on
fill3(P2x,P2y,repmat(zminmax(2),1,np),'r')
fill3(P1x,P1y,repmat(zminmax(1),1,np),'b')

So a right, trapezoidal frustrum, or something like that for a name.

[Rebekah Abrams]

As of right now, my code goes through each point to taper the shape. The code is the following where SOLIDX2 is a 27x67 matrix:

SOLIDX2(1:4,1:16) = 0.8* SOLIDX2(1:4,1:16); SOLIDX2(24:27,1:16) = 0.85* SOLIDX2(24:27,1:16);
SOLIDX2(1:4,1:4) = 1.01*SOLIDX2(1:4,1:4); SOLIDX2(24:27,1:4) = 1.02*SOLIDX2(24:27,1:4);
SOLIDX2(1:4,5) = 1.01*SOLIDX2(1:4,5); SOLIDX2(24:27,5) = 1.03*SOLIDX2(24:27,5);
SOLIDX2(1:4,6) = 1.03*SOLIDX2(1:4,6); SOLIDX2(24:27,6) = 1.07*SOLIDX2(24:27,6);
SOLIDX2(1:4,7) = 1.06*SOLIDX2(1:4,7); SOLIDX2(24:27,7) = 1.08*SOLIDX2(24:27,7);
SOLIDX2(1:4,8) = 1.09*SOLIDX2(1:4,8); SOLIDX2(24:27,8) = 1.09*SOLIDX2(24:27,8);
SOLIDX2(1:4,9) = 1.11*SOLIDX2(1:4,9); SOLIDX2(24:27,9) = 1.10*SOLIDX2(24:27,9);
SOLIDX2(1:4,10) = 1.13*SOLIDX2(1:4,10); SOLIDX2(24:27,10) = 1.11*SOLIDX2(24:27,10);
SOLIDX2(1:4,11) = 1.15*SOLIDX2(1:4,11); SOLIDX2(24:27,11) = 1.12*SOLIDX2(24:27,11);
SOLIDX2(1:4,12) = 1.17*SOLIDX2(1:4,12); SOLIDX2(24:27,12) = 1.13*SOLIDX2(24:27,12);
SOLIDX2(1:4,13) = 1.19*SOLIDX2(1:4,13); SOLIDX2(24:27,13) = 1.14*SOLIDX2(24:27,13);
SOLIDX2(1:4,14) = 1.21*SOLIDX2(1:4,14); SOLIDX2(24:27,14) = 1.15*SOLIDX2(24:27,14);
SOLIDX2(1:4,15) = 1.23*SOLIDX2(1:4,15); SOLIDX2(24:27,15) = 1.16*SOLIDX2(24:27,15);
SOLIDX2(1:4,16) = 1.25*SOLIDX2(1:4,16); SOLIDX2(24:27,16) = 1.17*SOLIDX2(24:27,16);
SOLIDX2(22:26,4) = SOLIDX2(22:26,5); SOLIDY2(22:26,4) = SOLIDY2(22:26,5);
SOLIDX2(22:26,3) = SOLIDX2(22:26,5); SOLIDY2(22:26,3) = SOLIDY2(22:26,5);
SOLIDX2(22:26,2) = SOLIDX2(22:26,5); SOLIDY2(22:26,2) = SOLIDY2(22:26,5);

Its very repetetive. I've been trying to turn this into a function so I could repeat it. The function I have as of right now is:

function [ SOLIDpiece1 ] = MidTaper( SOLIDX2,j,k )
%   This function should apply a tapered edge to the midfoot of the
%   orthotic using just the original matrix (SOLIDX2)

z = zeros(1,16) ;
n=1.01;
for i = 1:16

SOLIDX2piece1=SOLIDX2(j:k,1:i);
    if i == [1,1]
               z(i) = n*SOLIDX2(i,i) ;
    else
        SOLIDpiece1(i) = (n+(.2*i))*SOLIDX2piece1 ;
    end
end
end

However, I keep getting this error:

In an assignment  A(I) = B, the number of elements in B and I must be the same.

Error in MidTaper (line 14)
      SOLIDpiece1(i) = (n+(.2*i))*SOLIDX2piece1 ;

if you have any suggestions or how to tweak this, that would be incredible.