# Synopsis

PDX_MSGT gdx_ModelCurveToParmSpace(long option, int model, MDA_PTR sur, MDA_PTR modcur, double devtol, long maxits, int fdeg, void *parcurs, long *npc, double *moddev, T_GDX_RECT_MESH **rect_mesh)

# Purpose

Generate parameter space pre-image of model space curve(s).

# Description

Given a GDX surface S(u,v) and a GDX model space curve M(t) which lies on S(u,v) (to within some tolerance), this routine produces the parameter space curve P(s)=(u(s),v(s)), whose image under S(u,v) is the projection of M(t) onto S(u,v) to within the tolerance, devtol. S(u,v) and M(t) must be continuous, M(t) may have cusps, but S(u,v) must be smooth (no sharp ridges). Although P(s) will be a precise pre-image in some simple cases, it is generally an approximation (to within devtol). An iterative least squares curve fitting approach is used. The output curve, P(s), may consist of multiple curves, as it will be split where it crosses seams or poles. P(s) will be in Nurbs form.

The memory to contain parcurs is allocated by this function and must be freed by the caller. If the caller is not part of libgdx, this must be done by calling gdx_Free.

# Input

## option

### GDX_COMMIT

Entity creation option. If set, created entities will be commited to the data base.

### GDX_FITDEGMAX

If set, degree of P(s) will not exceed fdeg (see below). This will force the use of approximation in case degree of M(t) is greater than fdeg and S(u,v) is a plane. If not set, then a precise P(s) would be generated in this case (with degree(P(s)) = degree(M(t))).

### GDX_OPENCLOSED

If set, the surface will be treated as open in both directions.

### GDX_DEGREE_1

If set, the parametric curve generated always will be a Nurb curve of degree one.

## model

The GDX model for entity creation.

## sur

The GDX surface on which M(t) (modcur) lies.

## modcur

The model space curve, M(t), whose projection onto S(u,v) is to be mapped back into the uv-parameter space.

## devtol

The deviation of the model space image of P(s) from the projection of M(t) should not be greater than devtol. This tolerance should be larger than MODEL_SPACE_PNT_TOL, at least by 1 to 2 orders of magnitude.

## maxits

Maximum number of iterations. Iteration will be stopped if this number is exceeded.

## fdeg

Degree used for fitting the parameter space curve, P(s). See option GDX_FITDEGMAX above. If P(s) is a straight line, degree=1 will be used.

## rect_mesh

pointer to rect_mesh entity used as the temporary rect mesh for the projectsion or NULL. If non NULL is passed in first time, entitiy must be NULL.

# Output

## parcurs

An array of the Nurbs parameter space curves which make up P(s) (split at seams and poles). This allocated memory must be freed by caller, using gdx_Free if the caller is not part of libgdx.

## npc

Number of parameter space curves returned in parcurs.

## moddev

The measured deviation of M(t) from S(u,v).

## rect_mesh

if not NULL, it returns the rect mesh entity used for projection

# Tolerances

          MODEL_SPACE_PNT_TOL
          PARM_SPACE_PNT_TOL
          ANGLE_TOL
          ZERO_TOL
          .fi

# Return

          GDX_NOERR
          GDX_NOCONVERGE
          GDX_NOCURVE
          Low level error return
          .fi