Name

    SGIX_polynomial_ffd

Name Strings

    GL_SGIX_polynomial_ffd

Version

    $Date: 1996/03/01 22:13:06 $ $Revision: 1.15 $

Number

    59

Dependencies

    None

Overview

    This extension adds the capability to alter vertex coordinates,  the
    corresponding normal coordinates, and texture coordinates based on a
    client-specified trivariate polynomial functions.  These functions may be
    thought of as a warping of object/texture space (or, alternatively, as a
    warping of the object embedded in object/texture space).

    Deformations of space are used for a variety of modeling effects, including
    character animation.  The deformation specified in this extension is one of
    a variety of mappings that have been proposed.

    Only 3D to 3D deformation are considered.   We shall not consider
    homogeneous deformations.

Issues
    * Mark: Should there also be a 'target' parameter to allow for multiple
      (cumulative) deformations in the future?  (If yes, we need a new
      'get'.)

      Ziv: I think we can get away by 'naming' additional deformations as
      {GEOMETRY/TEXTURE}_DEFORMATION_XXX_SGIX and still use GetMap.

    * Mark: Limited memory may make it problematic to use both high-order
      evaluators and deformations at the same time.  The available memory could
      be traded off between deformations and evaluators (uh-oh --- do I smell an
      'evaluator object' extension coming?).

      Ziv: The RESOURCE_UNAVAILABLE error mechanism could solves this problem.
      Too bad it was reject from 1.1.  I am not clear about how we introduce it
      into an extension without having another extension.

    * Mark: Should deformations of texture, normal, and color coordinates be
      included as well.

      Ziv: As we already define normal deformations to be derived from the
      geometry deformation, independent normal deformations should not be
      included.  We do need Texture deformation however (e.g., for 3D
      textures), as texture and object space are different and are
      included. Color, being a non geometric entity does not seem to belong
      here.

    * Ziv: spec order issue.  The natural specification of deformations is in
      the Coordinate Transformations section - 2.9.  However, deformation use
      the description of Bernstein polynomials in evaluator section - 5.1 -
      creating an awkward forward reference.   In a formal spec the description
      of the polynomial would have to move from evaluators to the deformations
      sub-section.
      
New Procedures and Functions

    void DeformationMap3{fd}SGIX( enum target,
				  T u1, T u2, int ustride, int uorder,
				  T v1, T v2, int vstride, int vorder,
				  T w1, T w2, int wstride, int worder,
				  T* points);

    void LoadIdentityDeformationMapSGIX( bitfield mask );

    void DeformSGIX( bitfield mask );

New Tokens

    Accepted by the <target> parameter of DeformationMap3[fd]SGIX, and by the
    <target> parameter of GetMap:
    
        GEOMETRY_DEFORMATION_SGIX
        TEXTURE_DEFORMATION_SGIX

    Accepted by the <mask> parameter of DeformSGIX, and
    LoadIdentityDeformationMapSGIX:

        TEXTURE_DEFORMATION_BIT_SGIX		0x1
    	GEOMETRY_DEFORMATION_BIT_SGIX 		0x2

    Accepted by the <pname> parameter of GetBooleanv, GetIntegerv,
    GetFloatv, and GetDoublev:

    	DEFORMATIONS_MASK_SGIX
    	MAX_DEFORMATION_ORDER_SGIX
	
Additions to Chapter 2 of the 1.0 Specification (OpenGL Operation)

    Section 2.6.3, "GL Commands within Begin/End", is changed to include
    DeformSGIX in the list of commands allowed within Begin/End.
    
    The second paragraph of 2.9, "Coordinate Transformations," is replaced by
    (where Figure 2.6 is modified accordingly):

    Figure 2.6 diagrams the sequence of transformations that are applied to
    vertices.  The vertex coordinates that are presented to the GL are termed
    object coordinates.  The enabled geometry deformations (deformations are
    described in sub-section XXX, "Deformations") are applied to these
    coordinates to yield deformed object coordinates.  When no deformations are
    enabled it is as if an identity deformation is applied to the object
    coordinates.  Unless explicitly stated otherwise, in the rest of this
    document we will refer to deformed object coordinates as just object
    coordinates.  The model-view matrix is then applied to the object
    coordinates to yield eye coordinates.  Then another matrix, called the
    projection matrix, is applied to eye coordinates to yield clip coordinates.
    A perspective division is carried out on clip coordinates to yield
    normalized device coordinates.  A final viewport transformation is applied
    to convert these coordinates into window coordinates.

    A new sub-section entitled 'Deformations' is added after section 2.9.1:
    
    Deformations provide a means to use a polynomial mapping to transform
    vertex, normal, and texture coordinates.  When a deformation is applied to a
    4-tuple (c_0,c_1,c_2,c_3) the 3-tuple (c_0,c_1,c2) is transformed by a
    trivariate deformation map to another 3-tuple, while the c_3 remains
    unchanged.  The mapping of normals is not independent of the vertex mapping
    but is rather derived from the vertex deformation map.

    Let sum_{i=0}^l represent the sum over i from 0 to l.

    Consider the R^3-valued function:

    p(u,v,w)
      = sum_{i=0}^l sum_{j=0}^m sum_{k=0}^n B_i^l(u) B_j^m(v) B_k^n(w) R_ijk

    where B_i^j is a Bernstein polynomial as defined in equation 5.1.  The R_ijk
    are control points (as in equation 5.1); they correspond to the <points>
    specified with the DeformationMap3[fd]SGIX command.  <target> is one of the
    symbolic constants GEOMETRY_DEFORMATION_SGIX or TEXTURE_DEFORMATION_SGIX.
    <points> is a pointer to (l+1)(m+1)(n+1) blocks of storage (<uorder> = l+1,
    <vorder> = m+1, and <worder> = n+1).  The error INVALID_VALUE is generated
    if any of <uorder>, <vorder>, or <worder> is less than one, or if their
    product is greater than MAX_DEFORMATION_ORDER.  The three values comprising
    R_ijk are located at

	 <ustride>i + <vstride>j + <wstride>k

    values (either single- or double-precision floating-point, as appropriate)
    past the first value pointed to by <points>.

    <u1>, <u2>, <v1>, <v2>, <w1>, and <w2> define the pre-image of the
    the map; a domain point (u', v', w') is evaluated as

			  u' - <u1>    v' - <v1>    w' - <w1>
	p'(u',v',w') = p( -----------, -----------, -----------)
			  <u2> - <u1>  <v2> - <v1>  <w2> - <w1>

    The error INVALID_VALUE is generated if any of <ustride>, <vstride>, or
    <wstride> is less than 3, or if <u1> is equal to <u2>, <v1> is equal to
    <v2>, or if <w1> is equal to <w2>.

    Deformations are enabled and disabled using Deform.  The <mask> parameter is
    a bitwise OR of symbolic constants indicating which deformations are to be
    enabled.  The symbolic constants GEOMETRY_DEFORMATION_BIT_SGIX and
    TEXTURE_DEFORMATION_BIT_SGIX correspond to the geometry and texture
    deformations, respectively.  When a bit corresponding to a given deformation
    is 0, that deformation will be disabled.  The error INVALID_VALUE
    is generated if the <mask> contains bits other than
    GEOMETRY_DEFORMATION_BIT_SGIX and TEXTURE_DEFORMATION_BIT_SGIX.

    When enabled, geometry deformation maps (currently only one geometry
    deformation - GEOMETRY_DEFORMATION_SGIX - is defined) are applied to vertex
    coordinates immediately before the application of the model-view matrix.
    When a map is applied to a vertex the normal that is associated with that
    vertex is transformed as described below.  Enabled texture deformation maps
    (current only one texture deformation - TEXTURE_DEFORMATION_SGIX is defined)
    are applied to texture coordinates immediately prior to the application of
    the texture matrix.

    Normal coordinates are transformed by each enabled geometry deformation.
    The transformation proceeds by first computing the partial Jacobian matrix
    J of p' at the point (u', v', w'):

	J = ( dp'/du' dp'/dv' dp'/dw' )

    (p' is a column of 3 values, so dp'/ds is also).
    The transformed normal, n', is found from the untransformed normal,
    n = ( nx ny nz ), as

	n' = n J^{-1}.

    Note, that as deformations are defined to be applied immediately before the
    application model-view and texture matrices, they are therefore also applied
    to the vertices, normals, and textures resulting from EvalCoord and EvalMesh
    commands.

    LoadIdentityDeformation provides a quick method for setting
    deformations to the identity deformation.  The map for the
    deformations indicated by the <mask> parameter (with the same
    interpretation as in Deform) are set to the identity map.  The
    identity deformation maps are order 2 in each of u, v, and w, with
    <u1>=<v1>=<w1>=0 and <u2>=<v2>=<w2>=1, and the control point being
    (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1),
    (1, 1, 0), and (1, 1, 1).
    Note,  that unlike Deform, it is not an error for the mask to contain
    bits other than than GEOMETRY_DEFORMATION_BIT_SGIX and
    TEXTURE_DEFORMATION_BIT_SGIX.

    The state required for deformations is 2 3-dimensional map specification (as
    described by the call to DeformMap[fd]SGIX) and a bit mask indicating
    currently enabled deformations.  The maximum possible value for
    the product of <uorder>, <vorder>, and <worder> for each deformation type is
    implementation dependent but must be at least 1.  Initially, all the
    deformation maps are the identity map.

Additions to Chapter 3 of the 1.0 Specification (Rasterization)

    None

Additions to Chapter 4 of the 1.0 Specification (Per-Fragment Operations
and the Framebuffer)

    None

Additions to Chapter 5 of the 1.0 Specification (Special Functions)

    None

Additions to Chapter 6 of the 1.0 Specification (State and State Requests)

    None

GLX Protocol
	
    XXX - Not figured out yet.

Dependencies on other extensions

    None

Errors

    The error INVALID_ENUM is generated if the DeformationMap3[fd]SGIX <target>
    parameter is not GEOMETRY_DEFORMATION_SGIX or TEXTURE_DEFORMATION_SGIX.

    The error INVALID_VALUE is generated by DeformationMap3[fd]SGIX if:
	- any of <uorder>, <vorder>, or <worder> is less than one, or if their
	  product is greater than MAX_DEFORMATION_ORDER;
	- any of <ustride>, <vstride>, or <wstride> is less than 3;
	- <u1> is equal to <u2>, <v1> is equal to <v2>, or <w1> is equal
	  to <w2>. 
    
    The error INVALID_VALUE is generated by DeformSGIX if the <mask>
    contains bits other than GEOMETRY_DEFORMATION_BIT_SGIX and
    TEXTURE_DEFORMATION_BIT_SGIX.

    The error INVALID_OPERATION is generated if DeformationMap3[fd]SGIX is
    executed between execution of Begin and the corresponding execution of End.

New State

    Initial			Initial
    Get Value			Get Command	Type	  		Value 		Attrib
    ---------			-----------	----	  		-------		------
    ORDER			GetMap		2 x 3 x Z_1*		1,1,1		  -
    COEFF			GetMap		2 x 1* x 1* x 1* x R3	Sec X(2.9.1+)	  -
    DOMAIN			GetMap		2 x 6 x R		Sec X(2.9.1+)	  -
    DEFORMATION_MASK		GetIntegerv	F			0		transform

    - F is a new state variable type: a bitfield mask of flags.
    
New Implementation Dependent State
									Minimum
    Get Value				Get Command	Type		Value
    ---------				-----------	----		-------
    MAX_DEFORMATION_ORDER		GetInteger       Z                2