src/prism.civet

@@ -74,6 +74,15 @@ DEF Far Viewpoint {
 // Useful constants
 tau := 2*Math.PI
 
+// Array "postscript" operator
+operator ps<T>(main: T[], extra: T): T[]
+   main.push extra
+   main
+// Array "preface" operator
+operator pf<T>(extra: T, main: T[]): T[]
+   main.unshift extra
+   main
+
 function shIx(name: string): number
    shapeName.findIndex((sn) => name is in sn)
 
@@ -81,40 +90,149 @@ type ShapeMethod = (n: number, theta: number, d?: number) => string
 shapeMethod: ShapeMethod[] := []
 shapeMethods: Record<string, ShapeMethod> :=
    prism: (n, theta) =>
+      name := 'Prism'
       h := Math.sin theta/2
-      vrml: string[] := []
 
-      coords := orb(1, n, h, theta) ++ orb(1, n, -h, theta) ++ [[0,0,h], [0,0,-h]]
+      coords := orb(1, n, h, theta) ++ orb(1, n, -h, theta) ps [0,0,h] ps [0,0,-h]
       top := ([i, (i+1)%n, 2*n] for i of [0...n])
       bottom := ([(i+1)%n + n, i+n, 2*n+1] for i of [0...n])
-      firstFaces vrml, 'Prism', '0.8 0.7 0.5', coords, top ++ bottom
+      vrml := firstFaces name, '0.8 0.7 0.5', coords, top ++ bottom
 
       sides := ([i, (i+1)%n, (i+1)%n + n, i+n] for i of [0...n])
-      laterFaces vrml, 'Prism', '0.3 0.5 0.9', sides
-      laterLines vrml, 'Prism', sides
+      laterFaces vrml, name, '0.3 0.5 0.9', sides
+      laterLines vrml, name, sides
       emitObject vrml
 
    dipyr: (n, theta) =>
       name := 'Dipyramid'
       c := 1/Math.cos theta/2
       d := 1/Math.sin theta/2
-      vrml: string[] := []
 
-      coords := [[0,0,d]] ++ orb(c, n, 0, theta, 0.5) ++ [[0,0,-d]]
+      coords := [0,0,d] pf orb(c, n, 0, theta, 0.5) ps [0,0,-d]
       cap := ([0, i, i%n + 1] for i of [1..n])
       cup := ([i%n + 1, i, n+1] for i of [1..n])
-      firstFaces vrml, name, '0.9 0.3 0.3', coords, cap++cup
+      vrml := firstFaces name, '0.9 0.3 0.3', coords, cap++cup
 
-      edges := [[1..n]] ++ ([0, i, n+1] for i of [1..n])
+      edges := [1..n] pf ([0, i, n+1] for i of [1..n])
       laterLines vrml, name, edges
       emitObject vrml
 
    compound: (n, theta) =>
       shapeMethod[shIx 'prism'](n, theta) + shapeMethod[shIx 'dipyr'](n, theta)
 
+   antip: (n, theta) =>
+      name := 'Antiprism'
+      {h, r} := antiprismDims theta
+
+      coords := (orb(r, n, h, theta) ++ orb(r, n, -h, theta, 0.5)
+                 ps [0,0,h] ps [0,0,-h])
+      top := ([i, 2*n, (i+1)%n] for i of [0...n])
+      bottom := ([(i+1)%n + n, 2*n + 1, i+n] for i of [0...n])
+      vrml := firstFaces name, '0.8 0.7 0.5', coords, top ++ bottom
+
+      topsides := ([(i+1)%n, i+n, i] for i of [0...n])
+      botsides := ([i, i+n, (n+i-1)%n + n] for i of [0...n])
+      laterFaces vrml, name, '0.9 0.3 0.4', topsides ++ botsides
+      laterLines vrml, name, [[0...n] ps 0, [n...2*n] ps n, ...topsides]
+      emitObject vrml
+
+   trap: (n, theta) =>
+      name := 'Trapezohedron'
+      {h, r} := antiprismDims theta
+      [t, z] := dualPoint r*Math.cos(theta/2), h, r, -h
+
+      botzig := orb(t, n, -z, theta) ps [0, 0, -1/h]
+      topzig := orb(t, n, z, theta, 0.5) ps [0, 0, 1/h]
+      coords := alternate botzig, topzig
+      faces :=
+         for i of [0...2*n]
+            if i%2
+               [2*n + 1, (i+2)%(2*n), (i+1)%(2*n), i]
+            else [2*n, i, i+1, (i+2)%(2*n)]
+      vrml := firstFaces name, '0.3 0.5 0.9', coords, faces
+
+      edges :=
+         for i of [0...2*n]
+            i%2 ? [2*n + 1, i, (i + 1)%(2*n)] : [2*n, i, i+1]
+      laterLines vrml, name, edges
+      emitObject vrml
+
+   'antiprism + trap': (n, theta) =>
+      shapeMethod[shIx 'antip'](n, theta) + shapeMethod[shIx 'trap'](n, theta)
+
+   crossed: (n, theta) => // should really unify with antiprism, code is so close
+      name := 'CrossedAntiprism'
+      {h, r} := crossedDims theta
+
+      coords := (orb(r, n, h, theta) ++ orb(-r, n, -h, theta, 0.5)
+                 ps [0,0,h] ps [0,0,-h])
+      top := ([i, (i+1)%n, 2*n] for i of [0...n])
+      bottom := ([(i+1)%n + n, i+n, 2*n + 1] for i of [0...n])
+      vrml := firstFaces name, '0.8 0.7 0.5', coords, top ++ bottom
+
+      topsides := ([(i+1)%n, i+n, i] for i of [0...n])
+      botsides := ([i, i+n, (n+i-1)%n + n] for i of [0...n])
+      laterFaces vrml, name, '0.9 0.3 0.4', topsides ++ botsides
+      laterLines vrml, name, [[0...n] ps 0, [n...2*n] ps n, ...topsides]
+      emitObject vrml
+
+   concave: (n, theta, d) =>
+      name := 'ConcaveTrapezohedron'
+      {h, r} := crossedDims theta
+      [t, z] := dualPoint r*Math.cos(theta/2), h, -r, -h
+      d ??= Math.floor (n-1)/2  // won't be needed, for TypeScript's sake
+      eta := tau * (n-d)/n
+
+      botzig := orb(-t, n, -z, eta) ps [0, 0, -1/h]
+      topzig := orb(-t, n, z, eta, 0.5) ps [0, 0, 1/h]
+      coords := alternate botzig, topzig
+      halfFaces :=
+         for i of [0...2*n]
+            i%2 ? [(i+1)%(2*n), i, 2*n + 1] : [2*n, i, i+1]
+      otherFaces :=
+         for i of [0...2*n]
+            i%2 ? [2*n + 1, (i+2)%(2*n), (i+1)%(2*n)] : [2*n, i+1, (i+2)%(2*n)]
+      vrml := firstFaces name, '0.3 0.5 0.9', coords, halfFaces ++ otherFaces
+      laterLines vrml, name, halfFaces
+      emitObject vrml
+
+   'prism + concave': (n, theta, d) =>
+      shapeMethod[shIx 'cross'](n, theta) + shapeMethod[shIx 'conc'](n, theta, d)
+
+   polygon: (n, theta) =>
+      name := 'Polygon'
+      coords := orb(1, n, 0, theta) ps [0, 0, 0]
+      faces := ([i, (i+1)%n, n] for i of [0...n])
+      vrml := firstFaces name, '0.5 0.8 0.5', coords, faces
+      laterLines vrml, name, [[0...n] ps 0]
+      emitObject vrml
+
 for key, method in shapeMethods
    shapeMethod[shIx key] = method
 
+function antiprismDims(theta: number)
+   h .= Math.sqrt 1 - 4/(4 + 2*Math.cos(theta/2) - 2*Math.cos(theta))
+   r .= Math.sqrt 1 - h*h
+   f := Math.sqrt h*h + (r*Math.cos theta/2)**2
+   h /= f
+   r /= f
+   {h, r}
+
+function crossedDims(theta: number)
+   r .= 2/Math.sqrt 4 - 2*Math.cos(theta/2) - 2*Math.cos(theta)
+   h .= Math.sqrt 1 - r*r
+   f .= Math.sqrt h*h + (r*Math.cos theta/2)**2
+   r /= f
+   h /= f
+   {h, r}
+
+function dualPoint(x1: number, y1: number, x2: number, y2: number)
+   len := Math.sqrt (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1)
+   vx := (y2 - y1)/len
+   vy := (x1 - x2)/len
+   d := vx*x1 + vy*y1
+   [vx/d, vy/d]
+
 function vrmlBody(which: number, n: number, d: number)
    theta := tau * d/n
    shapeMethod[which](n, theta, d)
@@ -124,20 +242,26 @@ function orb(r: number, n: number, height: number, theta: number, t=0)
    for i of [0...n]
       [r*Math.cos(rho+i*theta), r*Math.sin(rho+i*theta), height]
 
-function firstFaces(container: string[], name: string, color: string,
-                    coords: number[][], faces: number[][]): void
-   startShape container, color
-   container.push 'geometry IndexedFaceSet {',
-      `coord DEF ${name}Coords Coordinate { point [`
-   container.push coord.join(' ') + ',' for each coord of coords
-   container.push '] }', 'creaseAngle 0 solid FALSE coordIndex ['
-   container.push face.join(', ') + ', -1,' for each face of faces
-   container.push '] } }'
+function alternate<T>(a: T[], b: T[])
+   return: T[] := []
+   return.value.push n, b[i] for each n, i of a
 
-function startShape(container: string[], color: string): void
+function firstFaces(name: string, color: string,
+                    coords: number[][], faces: number[][])
+   return: string[] := []
+   startShape return.value, color
+   return.value.push 'geometry IndexedFaceSet {',
+      `coord DEF ${name}Coords Coordinate { point [`
+   return.value.push coord.join(' ') + ',' for each coord of coords
+   return.value.push '] }',
+      'creaseAngle 0 solid FALSE coordIndex ['
+   return.value.push face.join(', ') + ', -1,' for each face of faces
+   return.value.push '] } }'
+
+function startShape(container: string[], color: string, colType = 'diffuse'): void
    container.push 'Shape { appearance Appearance {',
       '  material Material {',
-      `     diffuseColor ${color} } }`
+      `     ${colType}Color ${color} } }`
 
 function laterFaces(container: string[], name: string, color: string,
                     faces: number[][]): void
@@ -149,7 +273,7 @@ function laterFaces(container: string[], name: string, color: string,
    container.push '] } }'
 
 function laterLines(container: string[], name: string, edges: number[][]): void
-   startShape container, '0 0 0'
+   startShape container, '0 0 0', 'emissive'  // per VRML97 standard
    container.push 'geometry IndexedLineSet {',
       `coord USE ${name}Coords`,
       'coordIndex ['