Detailed Description

CAD utility functions and class definition for reconstruction of non-uniform rational bezier CAD objects.

This module supports internal refinement of CUBIT generated meshes while maintaining the true CAD boundary. Refinement uses MINPACK to minimize the weighted sum of distances between constraint points with the point constrained to the CAD object. Evaluation of CAD objects is provided by an interface to the OpenNURBS library.

Author: Chris Hansen

Date: May 2012

Data Types
type	nurbs_curve
	CAD curve class. More...

interface	nurbs_curve_domain
	Get the parametric domain of a NURBS curve. More...

interface	nurbs_curve_linear
	Test if NURBS curve is straight. More...

interface	nurbs_curve_name
	Get the name of a OpenNURBS curve. More...

interface	nurbs_curve_periodic
	Test periodicity of a NURBS curve. More...

interface	nurbs_dummy_eval
	Evaluate a NURBS object. More...

interface	nurbs_dummy_find
	Find the nearest location on a NURBS object to a given point. More...

interface	nurbs_dummy_grid
	Evalute a grid of points evenly spaced in parametric space. More...

interface	nurbs_dummy_unwrap
	Unwrap the periodic coordinates of a NURBS object to avoid parameter cuts. More...

interface	nurbs_dummy_wrap
	Wrap the periodic coordinates of a NURBS object into a single span. More...

type	nurbs_entity
	CAD entity class. More...

type	nurbs_entity_ptr
	List of CAD entities. More...

interface	nurbs_eval_curve
	Evalute the possition along a NURBS curve. More...

interface	nurbs_eval_surf
	Evalute the possition on a NURBS surface. More...

interface	nurbs_finalize
	Finalize the OpenNURBS library. More...

interface	nurbs_get_count
	Get a count of OpenNURBS objects in current file. More...

interface	nurbs_init
	Initialize the OpenNURBS library. More...

interface	nurbs_read_in
	Read-in a OpenNURBS *.3dm geometry file set objects as active. More...

type	nurbs_surf
	CAD surface class. More...

interface	nurbs_surf_domain
	Get the parametric domain of a NURBS surface. More...

interface	nurbs_surf_name
	Get the name of a OpenNURBS surface. More...

interface	nurbs_surf_periodic
	Test periodicity of a NURBS surface. More...

interface	nurbs_surf_planar
	Test if NURBS surface is planar. More...

interface	nurbs_surf_singular
	Test if edges of a NURBS surface are degenerate. More...

Functions/Subroutines
subroutine	nurbs_cmid_error (m, n, uv, err, iflag)
	Evalute the error between a curve point and the current active points used in a 2 point minimization.

subroutine	nurbs_curve_eval (self, pt, u, v)
	Map the parametric possition on a curve to physical coordinates.

subroutine	nurbs_curve_find (self, pt, u, v, ierr)
	Find the parametric representation of a boundary point in CAD representation on a curve.

subroutine	nurbs_curve_grid (self)
	Evalute a grid of points evenly spaced in parametric space.

subroutine, public	nurbs_curve_midpoint (self, pt, pt1, pt2, wt1, wt2, ierr)
	Compute the weighted midpoint of a curve edge.

subroutine	nurbs_curve_unwrap (self, u1, u2, v1, v2)
	Unwrap the coordinate of a periodic NURBS curve to avoid parameter cuts.

subroutine	nurbs_curve_wrap (self, u, v)
	Wrap the coordinate of a periodic NURBS curve into a single span.

subroutine	nurbs_scenter_error (m, n, uv, err, iflag)
	Evalute the error between a surface point and the current active points used in a 3 point minimization.

subroutine	nurbs_smid_error (m, n, uv, err, iflag)
	Evalute the error between a surface point and the current active points used in a 2 point minimization.

logical function	nurbs_surf_atsingular (self, u, v)
	Unwrap the periodic coordinates of a NURBS surface to avoid parameter cuts.

subroutine, public	nurbs_surf_avg (self, n, uin, vin, uavg, vavg)
	Unwrap the periodic coordinates of a NURBS surface to avoid parameter cuts.

subroutine, public	nurbs_surf_center (self, pt, pt1, pt2, pt3, wt1, wt2, wt3, ierr)
	Compute the weighted center point of a surface triangle.

subroutine	nurbs_surf_error (m, n, uv, err, iflag)
	Evalute the error between a surface point and the current active point used in a minimization.

subroutine	nurbs_surf_eval (self, pt, u, v)
	Map the parametric possition on a surface to physical coordinates.

subroutine	nurbs_surf_find (self, pt, u, v, ierr)
	Find the parametric representation of a boundary point in CAD representation on a surface.

subroutine	nurbs_surf_grid (self)
	Evalute a grid of points evenly spaced in parametric space.

subroutine, public	nurbs_surf_midpoint (self, pt, pt1, pt2, wt1, wt2, ierr)
	Compute the weighted midpoint of a surface edge.

subroutine	nurbs_surf_unwrap (self, u1, u2, v1, v2)
	Unwrap the periodic coordinates of a NURBS surface to avoid parameter cuts.

subroutine	nurbs_surf_wrap (self, u, v)
	Wrap the periodic coordinates of a NURBS surface into a single span.

Variables
class(nurbs_curve), pointer	active_curve => NULL()
	Active curve for MINPACK fitting.

real(r8), dimension(3, 3)	active_endpts
	Active constraint points for MINPACK fitting.

real(r8), dimension(3)	active_pt
	Active fit point for MINPACK fitting.

class(nurbs_surf), pointer	active_surf => NULL()
	Active surface for MINPACK fitting.

real(r8), dimension(3)	active_wts
	Active constraint weights for MINPACK fitting.

integer(i4), parameter	nurbs_ngrid = 20
	Number of grid points to use for object meshes.

real(r8), parameter	nurbs_singstep = .1d0
	Distance to offset guesses from singular edges.

Function/Subroutine Documentation

◆ nurbs_cmid_error()

subroutine nurbs_cmid_error	(	integer(i4), intent(in)	m,
		integer(i4), intent(in)	n,
		real(r8), dimension(n), intent(in)	uv,
		real(r8), dimension(m), intent(out)	err,
		integer(i4), intent(inout)	iflag
	)

private

Evalute the error between a curve point and the current active points used in a 2 point minimization.

Note: Designed to be used as the error function for minimization in nurbs_curve_midpoint

Parameters

[in]	m	Number of spatial dimensions (3)
[in]	n	Number of parametric dimensions (2)
[in]	uv	Parametric possition [n]
[out]	err	Error vector between current and desired point [3]
[in,out]	iflag	Unused flag

◆ nurbs_curve_eval()

subroutine nurbs_curve_eval	(	class(nurbs_curve), intent(in)	self,
		real(r8), dimension(3), intent(out)	pt,
		real(r8), intent(in)	u,
		real(r8), intent(in)	v
	)

private

Map the parametric possition on a curve to physical coordinates.

(u,v) -> (x,y,z)

Parameters

[out]	pt	Position vector [3]
[in]	u	Parametric coordinate 1
[in]	v	Parametric coordinate 2 (ignored)

◆ nurbs_curve_find()

subroutine nurbs_curve_find	(	class(nurbs_curve), intent(in), target	self,
		real(r8), dimension(3), intent(in)	pt,
		real(r8), intent(out)	u,
		real(r8), intent(out)	v,
		integer(i4), intent(out)	ierr
	)

private

Find the parametric representation of a boundary point in CAD representation on a curve.

(x,y,z) -> (u,v)

Parameters

[in]	pt	Position vector [3]
[out]	u	Parametric coordinate 1
[out]	v	Parametric coordinate 2 (ignored)

◆ nurbs_curve_grid()

subroutine nurbs_curve_grid ( class(nurbs_curve), intent(inout) self )

private

Evalute a grid of points evenly spaced in parametric space.

◆ nurbs_curve_midpoint()

subroutine, public nurbs_curve_midpoint	(	class(nurbs_curve), intent(in), target	self,
		real(r8), dimension(3), intent(inout)	pt,
		real(r8), dimension(3), intent(in)	pt1,
		real(r8), dimension(3), intent(in)	pt2,
		real(r8), intent(in)	wt1,
		real(r8), intent(in)	wt2,
		integer(i4), intent(out)	ierr
	)

Compute the weighted midpoint of a curve edge.

Locates the point on a given CAD curve which minimizes the weighted sum of distances to 2 constraint points.

\[ \sum_i w_i*(r_n - p_i)^2 \]

Parameters

[in]	self	CAD curve
[in,out]	pt	Solution point
[in]	pt1	Constraint point 1
[in]	pt2	Constraint point 2
[in]	wt1	Constraint weight 1
[in]	wt2	Constraint weight 2
[out]	ierr	Error flag

◆ nurbs_curve_unwrap()

subroutine nurbs_curve_unwrap	(	class(nurbs_curve), intent(in)	self,
		real(r8), intent(inout)	u1,
		real(r8), intent(inout)	u2,
		real(r8), intent(inout)	v1,
		real(r8), intent(inout)	v2
	)

private

Unwrap the coordinate of a periodic NURBS curve to avoid parameter cuts.

Example: For a periodic domain of \( [0,2 \pi] (3 \pi/4,0) -> (-\pi/4,0) \)

Parameters

[in,out]	u1	Parametric coordinate 1 of first point
[in,out]	v1	Parametric coordinate 2 of first point (unused)
[in,out]	u2	Parametric coordinate 1 of second point
[in,out]	v2	Parametric coordinate 2 of second point (unused)

◆ nurbs_curve_wrap()

subroutine nurbs_curve_wrap	(	class(nurbs_curve), intent(in)	self,
		real(r8), intent(inout)	u,
		real(r8), intent(inout)	v
	)

private

Wrap the coordinate of a periodic NURBS curve into a single span.

Example: For a periodic domain of \( [0,2 \pi] (-\pi/4,0) -> (3 \pi/4,0) \)

Parameters

[in,out]	u	Parametric coordinate 1
[in,out]	v	Parametric coordinate 2 (unused)

◆ nurbs_scenter_error()

subroutine nurbs_scenter_error	(	integer(i4), intent(in)	m,
		integer(i4), intent(in)	n,
		real(r8), dimension(n), intent(in)	uv,
		real(r8), dimension(m), intent(out)	err,
		integer(i4), intent(inout)	iflag
	)

private

Evalute the error between a surface point and the current active points used in a 3 point minimization.

Note: Designed to be used as the error function for minimization in nurbs_surf_center

Parameters

[in]	m	Number of spatial dimensions (3)
[in]	n	Number of parametric dimensions (2)
[in]	uv	Parametric possition [n]
[out]	err	Error vector between current and desired point [3]
[in,out]	iflag	Unused flag

◆ nurbs_smid_error()

subroutine nurbs_smid_error	(	integer(i4), intent(in)	m,
		integer(i4), intent(in)	n,
		real(r8), dimension(n), intent(in)	uv,
		real(r8), dimension(m), intent(out)	err,
		integer(i4), intent(inout)	iflag
	)

private

Evalute the error between a surface point and the current active points used in a 2 point minimization.

Note: Designed to be used as the error function for minimization in nurbs_surf_midpoint

Parameters

[in]	m	Number of spatial dimensions (3)
[in]	n	Number of parametric dimensions (2)
[in]	uv	Parametric possition [n]
[out]	err	Error vector between current and desired point [3]
[in,out]	iflag	Unused flag

◆ nurbs_surf_atsingular()

logical function nurbs_surf_atsingular	(	class(nurbs_surf), intent(in)	self,
		real(r8), intent(inout)	u,
		real(r8), intent(inout)	v
	)

private

Unwrap the periodic coordinates of a NURBS surface to avoid parameter cuts.

Example: For a periodic domain of \( [0,2 \pi] (3 \pi/4,0) -> (-\pi/4,0) \)

Parameters

[in,out]	u1	Parametric coordinate 1 of first point
[in,out]	v1	Parametric coordinate 2 of first point
[in,out]	u2	Parametric coordinate 1 of second point
[in,out]	v2	Parametric coordinate 2 of second point

◆ nurbs_surf_avg()

subroutine, public nurbs_surf_avg	(	class(nurbs_entity), intent(in), target	self,
		integer(i4), intent(in)	n,
		real(r8), dimension(n), intent(in)	uin,
		real(r8), dimension(n), intent(in)	vin,
		real(r8), intent(out)	uavg,
		real(r8), intent(out)	vavg
	)

Unwrap the periodic coordinates of a NURBS surface to avoid parameter cuts.

Example: For a periodic domain of \( [0,2 \pi] (3 \pi/4,0) -> (-\pi/4,0) \)

Parameters

[in,out]	u1	Parametric coordinate 1 of first point
[in,out]	v1	Parametric coordinate 2 of first point
[in,out]	u2	Parametric coordinate 1 of second point
[in,out]	v2	Parametric coordinate 2 of second point

◆ nurbs_surf_center()

subroutine, public nurbs_surf_center	(	class(nurbs_surf), intent(in), target	self,
		real(r8), dimension(3), intent(inout)	pt,
		real(r8), dimension(3), intent(in)	pt1,
		real(r8), dimension(3), intent(in)	pt2,
		real(r8), dimension(3), intent(in)	pt3,
		real(r8), intent(in)	wt1,
		real(r8), intent(in)	wt2,
		real(r8), intent(in)	wt3,
		integer(i4), intent(out)	ierr
	)

Compute the weighted center point of a surface triangle.

Locates the point on a given CAD surface which minimizes the weighted sum of distances to 3 constraint points.

\[ \sum_i w_i*(r_n - p_i)^2 \]

Parameters

[in]	self	CAD surface
[in,out]	pt	Solution point
[in]	pt1	Constraint point 1
[in]	pt2	Constraint point 2
[in]	pt3	Constraint point 3
[in]	wt1	Constraint weight 1
[in]	wt2	Constraint weight 2
[in]	wt3	Constraint weight 3
[out]	ierr	Error flag

◆ nurbs_surf_error()

subroutine nurbs_surf_error	(	integer(i4), intent(in)	m,
		integer(i4), intent(in)	n,
		real(r8), dimension(n), intent(in)	uv,
		real(r8), dimension(m), intent(out)	err,
		integer(i4), intent(inout)	iflag
	)

private

Evalute the error between a surface point and the current active point used in a minimization.

Note: Designed to be used with MINPACK for non-linear least square location of nearest surface point

Parameters

[in]	m	Number of spatial dimensions (3)
[in]	n	Number of parametric dimensions (2)
[in]	uv	Parametric possition [n]
[out]	err	Error vector between current and desired point [3]
[in,out]	iflag	Unused flag

◆ nurbs_surf_eval()

subroutine nurbs_surf_eval	(	class(nurbs_surf), intent(in)	self,
		real(r8), dimension(3), intent(out)	pt,
		real(r8), intent(in)	u,
		real(r8), intent(in)	v
	)

private

Map the parametric possition on a surface to physical coordinates.

(u,v) -> (x,y,z)

Parameters

[out]	pt	Position vector [3]
[in]	u	Parametric coordinate 1
[in]	v	Parametric coordinate 2

◆ nurbs_surf_find()

subroutine nurbs_surf_find	(	class(nurbs_surf), intent(in), target	self,
		real(r8), dimension(3), intent(in)	pt,
		real(r8), intent(out)	u,
		real(r8), intent(out)	v,
		integer(i4), intent(out)	ierr
	)

private

Find the parametric representation of a boundary point in CAD representation on a surface.

(x,y,z) -> (u,v)

Parameters

[in]	pt	Position vector [3]
[out]	u	Parametric coordinate 1
[out]	v	Parametric coordinate 2

◆ nurbs_surf_grid()

subroutine nurbs_surf_grid ( class(nurbs_surf), intent(inout) self )

private

Evalute a grid of points evenly spaced in parametric space.

◆ nurbs_surf_midpoint()

subroutine, public nurbs_surf_midpoint	(	class(nurbs_surf), intent(in), target	self,
		real(r8), dimension(3), intent(inout)	pt,
		real(r8), dimension(3), intent(in)	pt1,
		real(r8), dimension(3), intent(in)	pt2,
		real(r8), intent(in)	wt1,
		real(r8), intent(in)	wt2,
		integer(i4), intent(out)	ierr
	)

Compute the weighted midpoint of a surface edge.

Locates the point on a given CAD surface which minimizes the weighted sum of distances to 2 constraint points.

\[ \sum_i w_i*(r_n - p_i)^2 \]

Parameters

[in]	self	CAD surface
[in,out]	pt	Solution point
[in]	pt1	Constraint point 1
[in]	pt2	Constraint point 2
[in]	wt1	Constraint weight 1
[in]	wt2	Constraint weight 2
[out]	ierr	Error flag

◆ nurbs_surf_unwrap()

subroutine nurbs_surf_unwrap	(	class(nurbs_surf), intent(in)	self,
		real(r8), intent(inout)	u1,
		real(r8), intent(inout)	u2,
		real(r8), intent(inout)	v1,
		real(r8), intent(inout)	v2
	)

private

Unwrap the periodic coordinates of a NURBS surface to avoid parameter cuts.

Example: For a periodic domain of \( [0,2 \pi] (3 \pi/4,0) -> (-\pi/4,0) \)

Parameters

[in,out]	u1	Parametric coordinate 1 of first point
[in,out]	v1	Parametric coordinate 2 of first point
[in,out]	u2	Parametric coordinate 1 of second point
[in,out]	v2	Parametric coordinate 2 of second point

◆ nurbs_surf_wrap()

subroutine nurbs_surf_wrap	(	class(nurbs_surf), intent(in)	self,
		real(r8), intent(inout)	u,
		real(r8), intent(inout)	v
	)

private

Wrap the periodic coordinates of a NURBS surface into a single span.

Example: For a periodic domain of \( [0,2 \pi] (-\pi/4,0) -> (3 \pi/4,0) \)

Parameters

[in,out]	u	Parametric coordinate 1
[in,out]	v	Parametric coordinate 2

Variable Documentation

◆ active_curve

class(nurbs_curve), pointer active_curve => NULL()

private

Active curve for MINPACK fitting.

◆ active_endpts

real(r8), dimension(3,3) active_endpts

private

Active constraint points for MINPACK fitting.

◆ active_pt

real(r8), dimension(3) active_pt

private

Active fit point for MINPACK fitting.

◆ active_surf

class(nurbs_surf), pointer active_surf => NULL()

private

Active surface for MINPACK fitting.

◆ active_wts

real(r8), dimension(3) active_wts

private

Active constraint weights for MINPACK fitting.

◆ nurbs_ngrid

integer(i4), parameter nurbs_ngrid = 20

private

Number of grid points to use for object meshes.

◆ nurbs_singstep

real(r8), parameter nurbs_singstep = .1d0

private

Distance to offset guesses from singular edges.

Detailed Description

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ nurbs_cmid_error()

◆ nurbs_curve_eval()

◆ nurbs_curve_find()

◆ nurbs_curve_grid()

◆ nurbs_curve_midpoint()

◆ nurbs_curve_unwrap()

◆ nurbs_curve_wrap()

◆ nurbs_scenter_error()

◆ nurbs_smid_error()

◆ nurbs_surf_atsingular()

◆ nurbs_surf_avg()

◆ nurbs_surf_center()

◆ nurbs_surf_error()

◆ nurbs_surf_eval()

◆ nurbs_surf_find()

◆ nurbs_surf_grid()

◆ nurbs_surf_midpoint()

◆ nurbs_surf_unwrap()

◆ nurbs_surf_wrap()

Variable Documentation

◆ active_curve

◆ active_endpts

◆ active_pt

◆ active_surf

◆ active_wts

◆ nurbs_ngrid

◆ nurbs_singstep