Bezier Patch as a VBO (PShape)

Hardly needs introduction here is an alternative version of the bezier patch sketch, features ArcBall (arcball library is built in to my fork of ruby-processing, which is required to run a sketch with processing-2.0 functionality such as PShape) to rotate the patch and uses PShape object to store the geometry as a vbo.

# bezier bez_patch By Marius Watz:
# http://www.openprocessing.org/sketch/57709
# Normal calculation added by Andres Colubri
# Direct port of sample code by Paul Bourke.
# Original code: http://paulbourke.net/geometry/bezier/
#
# hit "spacebar" to generate a new shape and save current
#


load_library :vecmath

NI=4
NJ=5
RESI=NI*10
RESJ=NJ*10

attr_accessor :outp, :inp, :normp, :auto_normals, :arcball, :bez_patch


def setup
  size(1024, 768, P3D)
  @arcball = ArcBall.new(width/2.0, height/2.0, min(width - 20, height - 20) * 0.5)
  @auto_normals = false
  build_geometry
  @bez_patch = build_shape
end

def draw
  background(255)
  translate(width/2,height/2)
  smooth(8)
  lights
  define_lights
  #scale(0.9)
  update
  shape(bez_patch)
end

#######
# use bez patch geometry to
# create a vbo object (PShape)
#######

def build_shape
    no_stroke
    bez = create_shape(QUAD_STRIP)
    bez.fill(192, 192, 192)
    bez.ambient(20, 20, 20)
    (0 ... RESI - 1).each do |i|
        (0 ... RESJ).each do |j|
            if (!auto_normals)
                bez.normal(*normp[i][j])
            end
            bez.vertex(*outp[i][j])
            bez.vertex(*outp[i+1][j])
        end
    end
    bez.end     # end has unfortunate ruby highlighting in jedit, not in vim though
    return bez
end

##########
# build geometry
# for bez patch
##########

def build_geometry
  @outp = []
  @normp = []
  @inp = []
  uitang = PVector.new
  ujtang = PVector.new

  (0 ... NI).each do |i|
    row = Array.new
    (0 ... NJ).each do |j|
      row << PVector.new(i, j, (rand * 6) - 3)
    end
    inp << row
  end

  (0 ... RESI).each do |i|
    mui = i.fdiv(RESI - 1)
    row = []
    row_n = []
    (0 ... RESJ).each do |j|
      muj = j.fdiv(RESJ - 1)
      vect = PVector.new
      uitang.set(0, 0, 0)
      ujtang.set(0, 0, 0)
      (0 ... NI).each do |ki|
        bi = bezier_blend(ki, mui, NI)
        dbi = d_bezier_blend(ki, mui, NI)
        (0 ... NJ).each do |kj|
          bj = bezier_blend(kj, muj, NJ)
          dbj = d_bezier_blend(kj, muj, NJ)
          vect.x += (inp[ki][kj].x * bi * bj)
          vect.y += (inp[ki][kj].y * bi * bj)
          vect.z += (inp[ki][kj].z * bi * bj)

          uitang.x += (inp[ki][kj].x * dbi * bj)
          uitang.y += (inp[ki][kj].y * dbi * bj)
          uitang.z += (inp[ki][kj].z * dbi * bj)

          ujtang.x += (inp[ki][kj].x * bi * dbj)
          ujtang.y += (inp[ki][kj].y * bi * dbj)
          ujtang.z += (inp[ki][kj].z * bi * dbj)
        end
      end
      vect.add(PVector.new(-NI/2,-NJ/2,0))
      vect.mult(100)
      row << vect.array()
      uitang.normalize
      ujtang.normalize
      row_n << uitang.cross(ujtang).array()
    end
    @outp << row
    @normp << row_n
  end
end

def bezier_blend( k, mu,  n)
    blend = 1.0
    nn = n
    kn = k
    nkn = n - k

    while (nn >= 1)
        blend *= nn
        nn -= 1
        if (kn > 1)
            blend = blend.fdiv(kn)
            kn -= 1
        end
        if (nkn > 1)
            blend = blend.fdiv(nkn)
            nkn -= 1
        end
    end
    blend *= pow(mu, k.to_f) if (k > 0)
    blend *= pow(1-mu, (n - k).to_f) if (n - k > 0)
    return(blend)
end

def d_bezier_blend( k, mu,  n)
  dblendf = 1.0

  nn = n
  kn = k
  nkn = n - k

  while (nn >= 1)
    dblendf *= nn
    nn -= 1
    if (kn > 1)
      dblendf  = dblendf.fdiv(kn)
      kn -= 1
    end
    if (nkn > 1)
      dblendf  = dblendf.fdiv(nkn)
      nkn -= 1
    end
  end

  fk = 1
  dk = 0
  fnk = 1
  dnk = 0
  if (k > 0)
    fk = pow(mu, k.to_f)
    dk = k * pow(mu, (k - 1).to_f)
  end
  if (n - k > 0)
    fnk = pow(1 - mu, (n - k).to_f)
    dnk = (k - n)*pow(1 - mu, (n - k - 1).to_f)
  end
  dblendf *= (dk * fnk + fk * dnk)

  return(dblendf)
end

######################
# ArcBall control
# and lighting + re-run
######################

def update
    theta, x, y, z = arcball.update
    rotate(theta, x, y, z)
end

def mouse_pressed
    arcball.mouse_pressed(mouse_x, mouse_y)
end

def mouse_dragged
    arcball.mouse_dragged(mouse_x, mouse_y)
end

def define_lights
    ambient_light(60, 60, 60)
    point_light(30, 30, 30, 0, 0, 0)
    directional_light(40, 40, 50, 1, 0, 0)
    spot_light(30, 30, 30, 0, 40, 200, 0, -0.5, 0.5, PI / 2, 2)
end

def key_pressed
    case(key)
    when ' '
        save_frame("bezPatch.png")
        build_geometry
        @bez_patch = build_shape
    when 'x'
        arcball.select_axis(X)
    when 'y'
        arcball.select_axis(Y)
    when 'z'
        arcball.select_axis(Z)
    end
end

def key_released
    arcball.select_axis(-1)
end

Updated 20 February 2014 (arcball library is now in vecmath).