extensions/SGIX/SGIX_nurbs_eval.txt - external/github.com/KhronosGroup/OpenGL-Registry - Git at Google

 XXX - Not complete yet!!!
 Name

     SGIX_nurbs_eval

 Name Strings

     GL_SGIX_nurbs_eval

 Version

     $Date: 1998/02/12 18:24:45 $ $Revision: 1.6 $

 Number

     XXX

 Dependencies

     None

 Overview

     This extension adds a new evaluators type, NURBS.  NURBS are a compact
     representation of the datasets that many CAD and entertainment industry
     customers are already using.  The creation of a new interface allows for
     levels of performance not achievable with the current evaluators API.

     The current evaluators interface supports only Bezier curves, which suffer
     from several disadvantages:  Beziers are a wasteful of memory and graphics
     interface bandwidth; Beziers representations are often larger than
     the representations of the tesselated surfaces they are used to render;
     Beziers are not a native format used by CAD and entertainment applications.

     In the new NURBS extension, every effort has been made to extend the
     existing evaluators interface, rather than define a completely new set of
     interfaces and state.

 Issues

     * Should it be NURB or NURBS?

     I'm choosing NURBS since it matches the GLU spec and glu extensions.
     This does not agree with Farin's usage in the literature, but does agree
     with many other authors.

 New Procedures and Functions

     void NurbsKnots1SGIX[fd]( enum target,
 			      int uknotcount, T *uknots );
     void NurbsKnots2SGIX[fd]( enum target,
 			      int uknotcount, int vknotcount,
 			      T *uknots, T *vknots );

 New Tokens

     Accepted by the <cap> parameter of Enable, Disable, and IsEnabled, and
     by the <pname> parameter of GetBooleanv, GetIntegerv, GetFloatv, and
     GetDoublev:

 	MAP1_VERTEX_3_NURBS_SGIX	0x81CB
 	MAP1_VERTEX_4_NURBS_SGIX	0x81CC
 	MAP1_INDEX_NURBS_SGIX		0x81CD
 	MAP1_COLOR_4_NURBS_SGIX		0x81CE
 	MAP1_NORMAL_NURBS_SGIX		0x81CF
 	MAP1_TEXTURE_COORD_1_NURBS_SGIX	0x81E0
 	MAP1_TEXTURE_COORD_2_NURBS_SGIX	0x81E1
 	MAP1_TEXTURE_COORD_3_NURBS_SGIX	0x81E2
 	MAP1_TEXTURE_COORD_4_NURBS_SGIX	0x81E3
 	MAP2_VERTEX_3_NURBS_SGIX	0x81E4
 	MAP2_VERTEX_4_NURBS_SGIX	0x81E5
 	MAP2_INDEX_NURBS_SGIX		0x81E6
 	MAP2_COLOR_4_NURBS_SGIX		0x81E7
 	MAP2_NORMAL_NURBS_SGIX		0x81E8
 	MAP2_TEXTURE_COORD_1_NURBS_SGIX	0x81E9
 	MAP2_TEXTURE_COORD_2_NURBS_SGIX	0x81EA
 	MAP2_TEXTURE_COORD_3_NURBS_SGIX	0x81EB
 	MAP2_TEXTURE_COORD_4_NURBS_SGIX	0x81EC

     Accepted by the <value> parameter of GetMap[ifd]v:

 	NURBS_KNOT_COUNT_SGIX		0x81ED
 	NURBS_KNOT_VECTOR_SGIX		0x81EE

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

     None

 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 Frame Buffer)

     None

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

     Evaluators are extended to support both the existing specification, which
     is a Bezier formulation, and a new NURBS formulation.  New enable tokens
     are used to enable NURBS evaluation when it is desired.

   Basis Functions:

     NURBS polynomials for curves are defined as follows:
     Consider the R^k-valued polynomial q(u) is defined by
 	 q(u) = sum(i=0,n) N_i^d(u) * R_i
     with N_i^d(u) =    N_i^(d-1)(u) * (u-u(i-1))/(u(i+d-1)-u(i-1)) +
 		    N(i+1)^(d-1)(u) * (u(i+d)-u)/(u(i+d)-u_i)
     the i_th NURBS basis polynomial of degree d.

     Each R_i is a control point, and each u_i is a knot-value.
     The complete set of {u_i} values is called the knot vector.

   Map1[fd]:

     When NURBS evaluation is enabled, the <order> parameter to the Map1[fd]
     function is not really the mathematical order of the NURBS polynomial.
     Instead, the <order> parameter merely determines the size of the array
     given as input to Map1[fd] or Map2[fd].  In other words, the <order>
     parameter only determines the size of the valid GL state for the map
     array; it does not really capture the mathematical order of the curve or
     surface.

     Note that it is still true that the <order> parameter to Map1[fd] is equal
     to n+1 in the equation defining NURBS polynomials at the beginning of this
     section.

   Map2[fd]:

     NURBS polynomials for surfaces are defined as bivariate polynomials using
     the same N_i^d basis functions as NURBS curves:
 	q(u,v) = sum(i=0,n) sum(j=0,m) N_i^d(u) * N_j^c(v) * R_ij

   NurbsKnots1SGIX:
   NurbsKnots2SGIX:

     The <target> parameter must be one of GL_MAP1_VERTEX_3, GL_MAP1_VERTEX_4,
     GL_MAP1_COLOR_4, GL_MAP1_INDEX, GL_MAP1_NORMAL, GL_MAP1_TEXTURE_COORD_1,
     GL_MAP1_TEXTURE_COORD_2, GL_MAP1_TEXTURE_COORD_3, GL_MAP1_TEXTURE_COORD_4,
     GL_MAP2_VERTEX_3, GL_MAP2_VERTEX_4, GL_MAP2_COLOR_4, GL_MAP2_INDEX,
     GL_MAP2_NORMAL, GL_MAP2_TEXTURE_COORD_1, GL_MAP2_TEXTURE_COORD_2,
     GL_MAP2_TEXTURE_COORD_3, or GL_MAP2_TEXTURE_COORD_4.

     The knots vectors are defined by the new functions NurbsKnots1SGIX and
     NurbsKnots2SGIX.  The size of the knot vectors, <uknotcount> and
     <vknotcount> implicitly define the degree of the NURBS curves or surfaces
     defined.  For curves, the degree is defined as:
 	d = <uknotcount> - <uorder> + 1
     For surfaces, the second degree is defined as:
 	c = <vknotcount> - <vorder> + 1

     The entries from the <uknots> and <vknots> input arrays are immediately
     copied by the GL by the completion of this procedure.

   EvalCoord[12][fd]:
   EvalCoord[12][fd]v:
   EvalPoint[12]:
   EvalMesh[12]:

     For all of the new MAP1_XXX_NURBS tokens, when MAP1_XXX_NURBS is disabled,
     the evaluation functions, EvalCoord1[fd], EvalCoord1[fd]v, EvalPoint1, and
     EvalMesh1 all evaluate Bezier curves for the given map as usual.  When
     MAP1_XXX_NURBS is enabled, the evaluation functions instead evaluate NURBS
     curves.  Similarly, the new MAP2_XXX_NURBS tokens are used to enable NURBS
     surface evaluation for the functions EvalCoord2[fd], EvalCoord2[fd]v,
     EvalPoint2, and EvalMesh2.

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

     None

 Additions to the GLX Specification

     None

 GLX Protocol

     XXX - Not figured out yet.

 Dependencies on other extensions

     None

 Errors

     INVALID_VALUE is generated if NurbsKnots[12]SGIX parameter <uknotcount> or
     <vknotcount> are negative or greater that or equal to MAX_EVAL_ORDER.

     INVALID_VALUE is generated if <uorder> > <uknotcount>+1 when any of
     EvalCoord1[fd], EvalCoord1[fd]v, EvalPoint1, or EvalMesh1 are called if
     both of MAP1_XXX and MAP1_XXX_NURBS_SGIX are enabled.

     INVALID_VALUE is generated if <uorder> > <uknotcount>+1 or <vorder> >
     <vknotcount>+1 when any of EvalCoord2[fd], EvalCoord2[fd]v, EvalPoint2, or
     EvalMesh2 are called if both of MAP2_XXX and MAP2_XXX_NURBS_SGIX are
     enabled.

 New State

 									Initial
     Get Value				Get Command	Type	Value	Attrib
     ---------				-----------	----	-------	------
     MAP1_VERTEX_3_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP1_VERTEX_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP1_INDEX_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP1_COLOR_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP1_NORMAL_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP1_TEXTURE_COORD_1_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP1_TEXTURE_COORD_2_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP1_TEXTURE_COORD_3_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP1_TEXTURE_COORD_4_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP2_VERTEX_3_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP2_VERTEX_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP2_INDEX_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP2_COLOR_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP2_NORMAL_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
     MAP2_TEXTURE_COORD_1_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP2_TEXTURE_COORD_2_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP2_TEXTURE_COORD_3_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
     MAP2_TEXTURE_COORD_4_NURBS_SGIX	glIsEnabled	B	FALSE   eval/enable

     NURBS_KNOT_COUNT_SGIX		GetMapiv	9XZ+	 0
     NURBS_KNOT_COUNT_SGIX		GetMapiv	9X2XZ+	 0,0
     NURBS_KNOT_VECTOR_SGIX		GetMapdv	9X7*XR	 undef.
     NURBS_KNOT_VECTOR_SGIX		GetMapdv	9X2X7*XR undef.


 New Implementation Dependent State

     None
	XXX - Not complete yet!!!
	Name

	SGIX_nurbs_eval

	Name Strings

	GL_SGIX_nurbs_eval

	Version

	$Date: 1998/02/12 18:24:45 $ $Revision: 1.6 $

	Number

	XXX

	Dependencies

	None

	Overview

	This extension adds a new evaluators type, NURBS. NURBS are a compact
	representation of the datasets that many CAD and entertainment industry
	customers are already using. The creation of a new interface allows for
	levels of performance not achievable with the current evaluators API.

	The current evaluators interface supports only Bezier curves, which suffer
	from several disadvantages: Beziers are a wasteful of memory and graphics
	interface bandwidth; Beziers representations are often larger than
	the representations of the tesselated surfaces they are used to render;
	Beziers are not a native format used by CAD and entertainment applications.

	In the new NURBS extension, every effort has been made to extend the
	existing evaluators interface, rather than define a completely new set of
	interfaces and state.

	Issues

	* Should it be NURB or NURBS?

	I'm choosing NURBS since it matches the GLU spec and glu extensions.
	This does not agree with Farin's usage in the literature, but does agree
	with many other authors.

	New Procedures and Functions

	void NurbsKnots1SGIX[fd]( enum target,
	int uknotcount, T *uknots );
	void NurbsKnots2SGIX[fd]( enum target,
	int uknotcount, int vknotcount,
	T uknots, T vknots );

	New Tokens

	Accepted by the <cap> parameter of Enable, Disable, and IsEnabled, and
	by the <pname> parameter of GetBooleanv, GetIntegerv, GetFloatv, and
	GetDoublev:

	MAP1_VERTEX_3_NURBS_SGIX 0x81CB
	MAP1_VERTEX_4_NURBS_SGIX 0x81CC
	MAP1_INDEX_NURBS_SGIX 0x81CD
	MAP1_COLOR_4_NURBS_SGIX 0x81CE
	MAP1_NORMAL_NURBS_SGIX 0x81CF
	MAP1_TEXTURE_COORD_1_NURBS_SGIX 0x81E0
	MAP1_TEXTURE_COORD_2_NURBS_SGIX 0x81E1
	MAP1_TEXTURE_COORD_3_NURBS_SGIX 0x81E2
	MAP1_TEXTURE_COORD_4_NURBS_SGIX 0x81E3
	MAP2_VERTEX_3_NURBS_SGIX 0x81E4
	MAP2_VERTEX_4_NURBS_SGIX 0x81E5
	MAP2_INDEX_NURBS_SGIX 0x81E6
	MAP2_COLOR_4_NURBS_SGIX 0x81E7
	MAP2_NORMAL_NURBS_SGIX 0x81E8
	MAP2_TEXTURE_COORD_1_NURBS_SGIX 0x81E9
	MAP2_TEXTURE_COORD_2_NURBS_SGIX 0x81EA
	MAP2_TEXTURE_COORD_3_NURBS_SGIX 0x81EB
	MAP2_TEXTURE_COORD_4_NURBS_SGIX 0x81EC

	Accepted by the <value> parameter of GetMap[ifd]v:

	NURBS_KNOT_COUNT_SGIX 0x81ED
	NURBS_KNOT_VECTOR_SGIX 0x81EE

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

	None

	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 Frame Buffer)

	None

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

	Evaluators are extended to support both the existing specification, which
	is a Bezier formulation, and a new NURBS formulation. New enable tokens
	are used to enable NURBS evaluation when it is desired.

	Basis Functions:

	NURBS polynomials for curves are defined as follows:
	Consider the R^k-valued polynomial q(u) is defined by
	q(u) = sum(i=0,n) N_i^d(u) * R_i
	with N_i^d(u) = N_i^(d-1)(u) * (u-u(i-1))/(u(i+d-1)-u(i-1)) +
	N(i+1)^(d-1)(u) * (u(i+d)-u)/(u(i+d)-u_i)
	the i_th NURBS basis polynomial of degree d.

	Each R_i is a control point, and each u_i is a knot-value.
	The complete set of {u_i} values is called the knot vector.

	Map1[fd]:

	When NURBS evaluation is enabled, the <order> parameter to the Map1[fd]
	function is not really the mathematical order of the NURBS polynomial.
	Instead, the <order> parameter merely determines the size of the array
	given as input to Map1[fd] or Map2[fd]. In other words, the <order>
	parameter only determines the size of the valid GL state for the map
	array; it does not really capture the mathematical order of the curve or
	surface.

	Note that it is still true that the <order> parameter to Map1[fd] is equal
	to n+1 in the equation defining NURBS polynomials at the beginning of this
	section.

	Map2[fd]:

	NURBS polynomials for surfaces are defined as bivariate polynomials using
	the same N_i^d basis functions as NURBS curves:
	q(u,v) = sum(i=0,n) sum(j=0,m) N_i^d(u) * N_j^c(v) * R_ij

	NurbsKnots1SGIX:
	NurbsKnots2SGIX:

	The <target> parameter must be one of GL_MAP1_VERTEX_3, GL_MAP1_VERTEX_4,
	GL_MAP1_COLOR_4, GL_MAP1_INDEX, GL_MAP1_NORMAL, GL_MAP1_TEXTURE_COORD_1,
	GL_MAP1_TEXTURE_COORD_2, GL_MAP1_TEXTURE_COORD_3, GL_MAP1_TEXTURE_COORD_4,
	GL_MAP2_VERTEX_3, GL_MAP2_VERTEX_4, GL_MAP2_COLOR_4, GL_MAP2_INDEX,
	GL_MAP2_NORMAL, GL_MAP2_TEXTURE_COORD_1, GL_MAP2_TEXTURE_COORD_2,
	GL_MAP2_TEXTURE_COORD_3, or GL_MAP2_TEXTURE_COORD_4.

	The knots vectors are defined by the new functions NurbsKnots1SGIX and
	NurbsKnots2SGIX. The size of the knot vectors, <uknotcount> and
	<vknotcount> implicitly define the degree of the NURBS curves or surfaces
	defined. For curves, the degree is defined as:
	d = <uknotcount> - <uorder> + 1
	For surfaces, the second degree is defined as:
	c = <vknotcount> - <vorder> + 1

	The entries from the <uknots> and <vknots> input arrays are immediately
	copied by the GL by the completion of this procedure.

	EvalCoord[12][fd]:
	EvalCoord[12][fd]v:
	EvalPoint[12]:
	EvalMesh[12]:

	For all of the new MAP1_XXX_NURBS tokens, when MAP1_XXX_NURBS is disabled,
	the evaluation functions, EvalCoord1[fd], EvalCoord1[fd]v, EvalPoint1, and
	EvalMesh1 all evaluate Bezier curves for the given map as usual. When
	MAP1_XXX_NURBS is enabled, the evaluation functions instead evaluate NURBS
	curves. Similarly, the new MAP2_XXX_NURBS tokens are used to enable NURBS
	surface evaluation for the functions EvalCoord2[fd], EvalCoord2[fd]v,
	EvalPoint2, and EvalMesh2.

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

	None

	Additions to the GLX Specification

	None

	GLX Protocol

	XXX - Not figured out yet.

	Dependencies on other extensions

	None

	Errors

	INVALID_VALUE is generated if NurbsKnots[12]SGIX parameter <uknotcount> or
	<vknotcount> are negative or greater that or equal to MAX_EVAL_ORDER.

	INVALID_VALUE is generated if <uorder> > <uknotcount>+1 when any of
	EvalCoord1[fd], EvalCoord1[fd]v, EvalPoint1, or EvalMesh1 are called if
	both of MAP1_XXX and MAP1_XXX_NURBS_SGIX are enabled.

	INVALID_VALUE is generated if <uorder> > <uknotcount>+1 or <vorder> >
	<vknotcount>+1 when any of EvalCoord2[fd], EvalCoord2[fd]v, EvalPoint2, or
	EvalMesh2 are called if both of MAP2_XXX and MAP2_XXX_NURBS_SGIX are
	enabled.

	New State

	Initial
	Get Value Get Command Type Value Attrib
	--------- ----------- ---- ------- ------
	MAP1_VERTEX_3_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_VERTEX_4_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_INDEX_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_COLOR_4_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_NORMAL_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_TEXTURE_COORD_1_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_TEXTURE_COORD_2_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_TEXTURE_COORD_3_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP1_TEXTURE_COORD_4_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_VERTEX_3_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_VERTEX_4_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_INDEX_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_COLOR_4_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_NORMAL_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_TEXTURE_COORD_1_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_TEXTURE_COORD_2_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_TEXTURE_COORD_3_NURBS_SGIX glIsEnabled B FALSE eval/enable
	MAP2_TEXTURE_COORD_4_NURBS_SGIX glIsEnabled B FALSE eval/enable

	NURBS_KNOT_COUNT_SGIX GetMapiv 9XZ+ 0
	NURBS_KNOT_COUNT_SGIX GetMapiv 9X2XZ+ 0,0
	NURBS_KNOT_VECTOR_SGIX GetMapdv 9X7*XR undef.
	NURBS_KNOT_VECTOR_SGIX GetMapdv 9X2X7*XR undef.


	New Implementation Dependent State

	None