SET GLOBAL TRANSFORMATION 3(3P) — Kubota Pacfic Computer Inc. (29 February 1991)

NAME

SET GLOBAL TRANSFORMATION 3 − create structure element containing 3D global modelling transformation matrix

SYNOPSIS

C Syntax

void
pset_global_tran3 ( xform )
Pmatrix3xform;transformation matrix

Required PHIGS Operating States

(PHOP, ∗, STOP, ∗)

DESCRIPTION

Purpose

SET GLOBAL TRANSFORMATION 3 creates a structure element containing a 3D global modelling transformation matrix, which, during traversal, replaces the current global modelling transformation. Then the local modelling transformation is composed with the new global modelling transformation to create a new composite modelling transformation, which maps the modelling coordinates (MC) used to define individual output primitives to a unified world coordinate (WC) space.

If the current edit mode is INSERT, the SET GLOBAL TRANSFORMATION 3 element is inserted into the open structure after the element pointed to by the current element pointer. If the edit mode is REPLACE, the SET GLOBAL TRANSFORMATION 3 element replaces the element pointed to by the element pointer. In either case, the element pointer is updated to point to the new element.

C Input Parameter

xformThe 4 × 4 homogeneous transformation matrix (T), of type:

typedef Pfloat Pmatrix3[4][4];

Execution

When traversal of a structure begins, the initial current local modelling transformation (L) and the current global modelling transformation (G) are both the 3D, 4 × 4 identity matrix. The composite modelling transformation (C) within a structure traversal is formed by the matrix multiplication of the current local modelling transformation (L) and the current global modelling transformation (G) as follows:

C ← G × L

PHIGS assumes representation of points as column vectors. Hence, the order of composition in C ← G × L (and throughout) is “post-concatenation” or “post-multiply.”

When a new structure is traversed, one step in the invocation of the referenced structure is to save the current modelling transformations (L, G, and C). The child structure inherits the parent’s composite modelling transformation (C) as its current global modelling transformation (G), and an identity matrix as its initial current local modelling transformation (L). The parent and child have equal composite modelling transformations (C), because L is the identity. After traversal of the child structure network, the saved transformations are restored so that the parent is unaffected by the execution of a child.

When the SET GLOBAL TRANSFORMATION 3 element is traversed, the element’s transformation matrix (T) replaces the current global modelling transformation (G):

G´ ← T

The current local modelling transformation (L), is then composited with the new current global modelling transformation (G) to calculate the new composite modelling transformation (C).

C ← G´ × L

The current composite modelling transformation maps the modelling coordinates, used to define individual output primitives, to world coordinates. Mapping the primitives to the world coordinate space establishes the relation between different objects of the image by redefining the parts in terms of a unified coordinate space. This allows the application to define different parts of the image in different local modelling coordinates convenient to the objects being defined, and then to apply transformations that will map the local coordinate systems of each part to a single world coordinate (WC) space.

Finally, the viewing mechanism maps WC to device coordinates on the workstation’s physical display surface.

ERRORS

005Ignoring function, function requires state (PHOP, ∗, STOP, ∗)

Museum