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#### 4.2.4 Bezier Surfaces

The conventional file suffixes for Bezier surface files are `.bbp` or `.bez`. A file with either suffix may contain either type of patch.

Syntax:

           [ST]BBP -or- [C]BEZ<Nu><Nv><Nd>[_ST]
                                 # Nu, Nv are u- and v-direction
                                 # polynomial degrees in range 1..6
                                 # Nd = dimension: 3->3-D, 4->4-D (rational)
                                 # (The '<' and '>' do not appear in the input.)
                                 # Nu,Nv,Nd are each a single decimal digit.
                                 # BBP form implies Nu=Nv=Nd=3 so BBP = BEZ333.

                         # Any number of patches follow the header
                                 # (Nu+1)*(Nv+1) patch control points
                                 # each 3 or 4 floats according to header
           vertex(u=0,v=0)  vertex(1,0) ... vertex(Nu,0)
           vertex(0,1)                        ... vertex(Nu,1)
           ...
           vertex(0,Nv)                 ... vertex(Nu,Nv)

                                 # ST texture coordinates if mentioned in header
           S(u=0,v=0)     T(0,0)   S(0,Nv) T(0,Nv)
           S(Nu,0)  T(Nu,0)    S(Nu,Nv) T(Nu,Nv)

                                 # 4-component float (0..1) R G B A colors
                                 # for each patch corner if mentioned in header
           RGBA(0,0)   RGBA(0,Nv)
           RGBA(Nu,0)  RGBA(Nu,Nv)

These formats represent collections of Bezier surface patches, of degrees up to 6, and with 3-D or 4-D (rational) vertices.

The header keyword has the forms `[ST]BBP` or `[C]BEZ<`Nu`><`Nv`><`Nd`>[_ST]` (the '<' and '>' are not part of the keyword.

The `ST` prefix on `BBP`, or `_ST` suffix on `BEZuvn`, indicates that each patch includes four pairs of floating-point texture-space coordinates, one for each corner of the patch.

The `C` prefix on `BEZuvn` indicates a colored patch, including four sets of four-component floating-point colors (red, green, blue, and alpha) in the range 0..1, one color for each corner.

Nu and Nv, each a single digit in the range 1..6, are the patch's polynomial degree in the u and v direction respectively.

Nd is the number of components in each patch vertex, and must be either `3` for 3-D or `4` for homogeneous coordinates, that is, rational patches.

`BBP` patches are bicubic patches with 3-D vertices, so `BBP` = `BEZ333` and `STBBP` = `BEZ333_ST`.

Any number of patches follow the header. Each patch comprises a series of patch vertices, followed by optional (s,t) texture coordinates, followed by optional (r,g,b,a) colors.

Each patch has (Nu+1)*(Nv+1) vertices in v-major order, so that if we designate a vertex by its control point indices (u,v) the order is

              (0,0) (1,0) (2,0) ...  (Nu,0)
              (0,1) (1,1) (2,1) ...  (Nu,1)
              ...
              (0,Nv)            ...  (Nu,Nv)

with each vertex containing either 3 or 4 floating-point numbers as specified by the header.

If the header calls for ST coordinates, four pairs of floating-point numbers follow: the texture-space coordinates for the (0,0), (Nu,0), (0,Nv), and (Nu,Nv) corners of the patch, respectively.

If the header calls for colors, four four-component (red, green, blue, alpha) floating-point colors follow, one for each patch corner.

The series of patches ends at end-of-file, or with a closebrace if incorporated in an object reference.