spec_obj.txt

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format:

o       Bezier

o       basis matrix

o       B-spline

o       Cardinal

o       Taylor

You can apply these types only to curves and surfaces. Each of these
five types can be rational or non-rational.

In addition to specifying the type, you must define the degree for the
curve or surface. For basis matrix curve and surface elements, you must
also specify the basis matrix and step size.

All free-form curve and surface attribute statements are state-setting.
This means that once an attribute statement is set, it applies to all
elements that follow until it is reset to a different value.

Syntax

The following syntax statements are listed in order of use.

cstype rat type

    Free-form geometry statement.

    Specifies the type of curve or surface and indicates a rational or
    non-rational form.

    rat is an optional argument.

    rat specifies a rational form for the curve or surface type. If rat
    is not included, the curve or surface is non-rational

    type specifies the curve or surface type. Allowed types are:

	bmatrix		basis matrix

	bezier		Bezier

	bspline		B-spline

	cardinal        Cardinal

	taylor		Taylor

    There is no default. A value must be supplied.

deg degu degv

    Free-form geometry statement.

    Sets the polynomial degree for curves and surfaces.

    degu is the degree in the u direction. It is required for both
    curves and surfaces.

    degv is the degree in the v direction. It is required only for
    surfaces. For Bezier, B-spline, Taylor, and basis matrix, there is
    no default; a value must be supplied. For Cardinal, the degree is
    always 3. If some other value is given for Cardinal, it will be
    ignored.

bmat u matrix

bmat v matrix

    Free-form geometry statement.

    Sets the basis matrices used for basis matrix curves and surfaces.
    The u and v values must be specified in separate bmat statements.

    NOTE: The deg statement must be given before the bmat statements
    and the size of the matrix must be appropriate for the degree.

    u specifies that the basis matrix is applied in the u direction.

    v specifies that the basis matrix is applied in the v direction.

    matrix lists the contents of the basis matrix with column subscript
    j varying the fastest. If n is the degree in the given u or v
    direction, the matrix (i,j) should be of size (n + 1) x (n + 1).

    There is no default. A value must be supplied.

    NOTE: The arrangement of the matrix is different from that commonly
    found in other references. For more information, see the examples
    at the end of this section and also the section, "Mathematics for
    free-form curves and surfaces."

step stepu stepv

    Free-form geometry statement.

    Sets the step size for curves and surfaces that use a basis
    matrix.

    stepu is the step size in the u direction. It is required for both
    curves and surfaces that use a basis matrix.

    stepv is the step size in the v direction. It is required only for
    surfaces that use a basis matrix. There is no default. A value must
    be supplied.

    When a curve or surface is being evaluated and a transition from
    one segment or patch to the next occurs, the set of control points
    used is incremented by the step size. The appropriate step size
    depends on the representation type, which is expressed through the
    basis matrix, and on the degree.

    That is, suppose we are given a curve with k control points:
			{v , ... v }
			  1       k

    If the curve is of degree n, then n + 1 control points are needed
    for each polynomial segment. If the step size is given as s, then
    the ith polynomial segment, where i = 0 is the first segment, will
    use the control points:
			{v    ,...,v      }
			  is+1      is+n+1

    For example, for Bezier curves, s = n .

    For surfaces, the above description applies independently to each
    parametric direction.

    When you create a file which uses the basis matrix type, be sure to
    specify a step size appropriate for the current curve or surface
    representation.

Examples

1.      Cubic Bezier surface made with a basis matrix

    To create a cubic Bezier surface:

	cstype bmatrix
	deg 3 3
	step 3 3
	bmat u  1       -3      3       -1      \
		0       3       -6      3       \
		0       0       3       -3      \
		0       0       0       1
	bmat v  1       -3      3       -1      \
		0       3       -6      3       \
		0       0       3       -3      \
		0       0       0       1

2.      Hermite curve made with a basis matrix

    To create a Hermite curve:

	cstype bmatrix
	deg 3
	step 2
	bmat u  1     0     -3      2      0       0       3      -2 \
		0     1     -2      1      0       0      -1       1

3.      Bezier in u direction with B-spline in v direction;
	made with a basis matrix

    To create a surface with a cubic Bezier in the u direction and
    cubic uniform B-spline in the v direction:

	cstype bmatrix
	deg 3 3
	step 3 1
	bmat u  1      -3       3      -1 \
		0       3      -6       3 \
		0       0       3      -3 \
		0       0       0       1
	bmat v  0.16666 -0.50000  0.50000 -0.16666 \
		0.66666  0.00000 -1.00000  0.50000 \
		0.16666  0.50000  0.50000 -0.50000 \
		0.00000  0.00000  0.00000  0.16666



Elements

For polygonal geometry, the element types available in the .obj file
are:

o       points

o       lines

o       faces

For free-form geometry, the element types available in the .obj file
are:

o       curve

o       2D curve on a surface

o       surface

All elements can be freely intermixed in the file.

Referencing vertex data

For all elements, reference numbers are used to identify geometric
vertices, texture vertices, vertex normals, and parameter space
vertices.

Each of these types of vertices is numbered separately, starting with
1. This means that the first geometric vertex in the file is 1, the
second is 2, and so on. The first texture vertex in the file is 1, the
second is 2, and so on. The numbering continues sequentially throughout
the entire file. Frequently, files have multiple lists of vertex data.
This numbering sequence continues even when vertex data is separated by
other data.

In addition to counting vertices down from the top of the first list in
the file, you can also count vertices back up the list from an
element's position in the file. When you count up the list from an
element, the reference numbers are negative. A reference number of -1
indicates the vertex immediately above the element. A reference number
of -2 indicates two references above and so on.

Referencing groups of vertices

Some elements, such as faces and surfaces, may have a triplet of
numbers that reference vertex data.These numbers are the reference
numbers for a geometric vertex, a texture vertex, and a vertex normal.

Each triplet of numbers specifies a geometric vertex, texture vertex,
and vertex normal. The reference numbers must be in order and must
separated by slashes (/).

o       The first reference number is the geometric vertex.

o       The second reference number is the texture vertex. It follows
	the first slash.

o       The third reference number is the vertex normal. It follows the
	second slash.

There is no space between numbers and the slashes. There may be more
than one series of geometric vertex/texture vertex/vertex normal
numbers on a line.

The following is a portion of a sample file for a four-sided face
element:

    f 1/1/1 2/2/2 3/3/3 4/4/4

Using v, vt, and vn to represent geometric vertices, texture vertices,
and vertex normals, the statement would read:

    f v/vt/vn v/vt/vn v/vt/vn v/vt/vn

If there are only vertices and vertex normals for a face element (no
texture vertices), you would enter two slashes (//). For example, to
specify only the vertex and vertex normal reference numbers, you would
enter:

    f 1//1 2//2 3//3 4//4

When you are using a series of triplets, you must be consistent in the
way you reference the vertex data. For example, it is illegal to give
vertex normals for some vertices, but not all.

The following is an example of an illegal statement.

    f 1/1/1 2/2/2 3//3 4//4

Syntax

The following syntax statements are listed in order of complexity of
geometry.

p  v1 v2 v3 . . .

    Polygonal geometry statement.

    Specifies a point element and its vertex. You can specify multiple
    points with this statement. Although points cannot be shaded or
    rendered, they are used by other Advanced Visualizer programs.

    v is the vertex reference number for a point element. Each point
    element requires one vertex. Positive values indicate absolute
    vertex numbers. Negative values indicate relative vertex numbers.

l  v1/vt1   v2/vt2   v3/vt3 . . .

    Polygonal geometry statement.

    Specifies a line and its vertex reference numbers. You can
    optionally include the texture vertex reference numbers. Although
    lines cannot be shaded or rendered, they are used by other Advanced
    Visualizer programs.

    The reference numbers for the vertices and texture vertices must be
    separated by a slash (/). There is no space between the number and
    the slash.

    v is a reference number for a vertex on the line. A minimum of two
    vertex numbers are required. There is no limit on the maximum.
    Positive values indicate absolute vertex numbers. Negative values
    indicate relative vertex numbers.

    vt is an optional argument.

    vt is the reference number for a texture vertex in the line
    element. It must always follow the first slash.

f  v1/vt1/vn1   v2/vt2/vn2   v3/vt3/vn3 . . .

    Polygonal geometry statement.

    Specifies a face element and its vertex reference number. You can
    optionally include the texture vertex and vertex normal reference
    numbers.

    The reference numbers for the vertices, texture vertices, and
    vertex normals must be separated by slashes (/). There is no space
    between the number and the slash.

    v is the reference number for a vertex in the face element. A
    minimum of three vertices are required.

    vt is an optional argument.

    vt is the reference number for a texture vertex in the face
    element. It always follows the first slash.

    vn is an optional argument.

    vn is the reference number for a vertex normal in the face element.
    It must always follow the second slash.

    Face elements use surface normals to indicate their orientation. If
    vertices are ordered counterclockwise around the face, both the
    face and the normal will point toward the viewer. If the vertex
    ordering is clockwise, both will point away from the viewer. If
    vertex normals are assigned, they should point in the general
    direction of the surface normal, otherwise unpredictable results
    may occur.

    If a face has a texture map assigned to it and no texture vertices
    are assigned in the f statement, the texture map is ignored when
    the element is rendered.

    NOTE: Any references to fo (face outline) are no longer valid as of
    version 2.11. You can use f (face) to get the same results.
    References to fo in existing .obj files will still be read,
    however, they will be written out as f when the file is saved.

curv u0 u1 v1 v2 . . .

    Element statement for free-form geometry.

    Specifies a curve, its parameter range, and its control vertices.
    Although curves cannot be shaded or rendered, they are used by
    other Advanced Visualizer programs.

    u0 is the starting parameter value for the curve. This is a
    floating point number.

    u1 is the ending parameter value for the curve. This is a floating
    point number.

    v is the vertex reference number for a control point. You can
    specify multiple control points. A minimum of two control points
    are required for a curve.

    For a non-rational curve, the control points must be 3D. For a
    rational curve, the control points are 3D or 4D. The fourth
    coordinate (weight) defaults to 1.0 if omitted.

curv2  vp1  vp2   vp3. . .

    Free-form geometry statement.

    Specifies a 2D curve on a surface and its control points. A 2D
    curve is used as an outer or inner trimming curve, as a special
    curve, or for connectivity.

    vp is the parameter vertex reference number for the control point.
    You can specify multiple control points. A minimum of two control
    points is required for a 2D curve.

    The control points are parameter vertices because the curve must
    lie in the parameter space of some surface. For a non-rational
    curve, the control vertices can be 2D. For a rational curve, the
    control vertices can be 2D or 3D. The third coordinate (weight)
    defaults to 1.0 if omitted.

surf  s0  s1  t0  t1  v1/vt1/vn1   v2/vt2/vn2 . . .

    Element statement for free-form geometry.

    Specifies a surface, its parameter range, and its control vertices.
    The surface is evaluated within the global parameter range from s0
    to s1 in the u direction and t0 to t1 in the v direction.

    s0 is the starting parameter value for the surface in the u
    direction.

    s1 is the ending parameter value for the surface in the u
    direction.

    t0 is the starting parameter value for the surface in the v
    direction.

    t1 is the ending parameter value for the surface in the v
    direction.

    v is the reference number for a control vertex in the surface.

    vt is an optional argument.

    vt is the reference number for a texture vertex in the surface.  It
    must always follow the first slash.

    vn is an optional argument.

    vn is the reference number for a vertex normal in the surface.  It
    must always follow the second slash.

    For a non-rational surface, the control vertices are 3D.  For a
    rational surface the control vertices can be 3D or 4D.  The fourth
    coordinate (weight) defaults to 1.0 if ommitted.

    NOTE: For more information on the ordering of control points for