skia / external / github.com / KhronosGroup / OpenGL-Registry / eae1d6dde1e283f6fdf803274a2484007e592599 / . / extensions / SGIX / SGIX_polynomial_ffd.txt

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 | |