Partially slice 3D rendered donut along its polodial direction

donut.lua

@@ -6,7 +6,7 @@
 
 -- cargo-culted by erle 2023-09-18
 
-local theta_spacing = 0.1  -- 0.07
+local theta_spacing = 0.01  -- 0.07
 local phi_spacing = 0.002  -- 0.02
 
 local R1 = 1
@@ -43,13 +43,25 @@ function render_frame(A, B)
    local sinB = math.sin(B)
 
    -- theta goas around the cross-sectional circle of a torus
-   for theta=0, 2*math.pi, theta_spacing do
+   local theta = 0
+   while theta <= 2*math.pi do
+      if ( theta < 2*math.pi * 1/8 ) or ( theta > 2*math.pi * 7/8 ) then
+         theta = theta + (theta_spacing * 16)
+      else
+         theta = theta + theta_spacing
+      end
       -- precompute sines and cosines of theta
       local costheta = math.cos(theta)
       local sintheta = math.sin(theta)
 
       -- phi goes around the center of revolution of a torus
-      for phi=0, 2*math.pi, phi_spacing do
+      local phi = 0
+      while phi <= 2*math.pi do
+         if ( phi > 2*math.pi * 3/8 ) and ( phi < 2*math.pi * 5/8 ) then
+            phi = phi + (phi_spacing * 128)
+         else
+            phi = phi + phi_spacing
+         end
         -- precompute sines and cosines of phi
          local cosphi = math.cos(phi)
          local sinphi = math.sin(phi)