Detailed Description

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

This module supports internal refinement of T3D 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.

Author: Chris Hansen

Date: June 2010

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

interface	cad_dummy_eval
	Map the parametric possition on an entity to physical coordinates. More...

interface	cad_dummy_find
	Find the parametric representation of a boundary point in CAD representation. More...

type	cad_entity
	CAD entity class. More...

type	cad_entity_ptr
	List of CAD entities. More...

type	cad_surf
	CAD surface class. More...

type	cad_vertex
	CAD vertex class. More...

Functions/Subroutines
real(r8) function, public	bernstein (x, i, j)
	Evaluates the bernstein polynomial.

subroutine	cad_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.

integer(i4) function, public	cad_curve_cast (self, source)
	Cast cad_entity to cad_curve.

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

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

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

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

subroutine	cad_curve_reflect (self, copy, tol, k)
	Reflect a curve object across a given plane.

subroutine	cad_curve_tang (self, tang, u)
	Compute unit tangent vector for a CAD curve at a given location.

subroutine	cad_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	cad_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.

integer(i4) function, public	cad_surf_cast (self, source)
	Cast cad_entity to cad_surf.

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

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

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

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

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

subroutine	cad_surf_norm (self, norm, u, v)
	Compute unit normal vector for a CAD surface at a specified position.

subroutine	cad_surf_reflect (self, copy, tol, k)
	Reflect a surface object across a given plane.

subroutine	cad_vertex_eval (self, pt, u, v)
	Map parametric possition of a vertex to physical coordinates.

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

subroutine	cad_vertex_reflect (self, copy, tol, k)
	Reflect a vertex object across a given plane.

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

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

class(cad_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	cad_ngrid = 20
	Number of grid points to use for object meshes.

Function/Subroutine Documentation

◆ bernstein()

real(r8) function, public bernstein	(	real(r8), intent(in)	x,
		integer(i4), intent(in)	i,
		integer(i4), intent(in)	j
	)

Evaluates the bernstein polynomial.

f(x) = \( B_{ij}(x) \)

Returns: \( B_{ij}(x) \)

Parameters

[in]	x	Point to evaluate
[in]	i	Polynomial degree
[in]	j	Polynomial kind

◆ cad_cmid_error()

subroutine cad_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 cad_curve_midpoint

Parameters

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

◆ cad_curve_cast()

integer(i4) function, public cad_curve_cast	(	class(cad_curve), intent(out), pointer	self,
		class(cad_entity), intent(in), target	source
	)

Cast cad_entity to cad_curve.

Returns: Error flag

Parameters

[out]	self	Object of desired type, unassociated if cast fails
[in]	source	Source object to cast

◆ cad_curve_eval()

subroutine cad_curve_eval	(	class(cad_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)

◆ cad_curve_find()

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

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)

◆ cad_curve_grid()

subroutine cad_curve_grid ( class(cad_curve), intent(inout) self )

private

Evalute a grid of points evenly spaced in parametric space.

◆ cad_curve_midpoint()

subroutine, public cad_curve_midpoint	(	class(cad_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	Curve object
[in,out]	pt	Solution point [3]
[in]	pt1	Constraint point 1 [3]
[in]	pt2	Constraint point 2 [3]
[in]	wt1	Weight for constraint point 1
[in]	wt2	Weight for constraint point 2
[out]	ierr	Error flag

◆ cad_curve_reflect()

subroutine cad_curve_reflect	(	class(cad_curve), intent(in)	self,
		class(cad_curve), intent(out)	copy,
		real(r8), intent(in)	tol,
		integer(i4), intent(in)	k
	)

private

Reflect a curve object across a given plane.

Parameters

[in]	self	Source object to copy
[out]	copy	Reflected copy of the source curve
[in]	tol	Minimum distance from plane
[in]	k	Coordinate index for the reflection plane

◆ cad_curve_tang()

subroutine cad_curve_tang	(	class(cad_curve), intent(in)	self,
		real(r8), dimension(3), intent(out)	tang,
		real(r8), intent(in)	u
	)

private

Compute unit tangent vector for a CAD curve at a given location.

Parameters

[out]	tang	Curve tangent unit vector [3]
[in]	u	Parametric coordinate

◆ cad_scenter_error()

subroutine cad_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 cad_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

◆ cad_smid_error()

subroutine cad_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 cad_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

◆ cad_surf_cast()

integer(i4) function, public cad_surf_cast	(	class(cad_surf), intent(out), pointer	self,
		class(cad_entity), intent(in), target	source
	)

Cast cad_entity to cad_surf.

Returns: Error flag

Parameters

[out]	self	Object of desired type, unassociated if cast fails
[in]	source	Source object to cast

◆ cad_surf_center()

subroutine, public cad_surf_center	(	class(cad_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	Surface object
[in,out]	pt	Solution point [3]
[in]	pt1	Constraint point 1 [3]
[in]	pt2	Constraint point 2 [3]
[in]	pt3	Constraint point 3 [3]
[in]	wt1	Weight for constraint point 1
[in]	wt2	Weight for constraint point 2
[in]	wt3	Weight for constraint point 3
[out]	ierr	Error flag

◆ cad_surf_eval()

subroutine cad_surf_eval	(	class(cad_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

◆ cad_surf_find()

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

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

◆ cad_surf_grid()

subroutine cad_surf_grid ( class(cad_surf), intent(inout) self )

private

Evalute a grid of points evenly spaced in parametric space.

◆ cad_surf_midpoint()

subroutine, public cad_surf_midpoint	(	class(cad_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	Surface object
[in,out]	pt	Solution point [3]
[in]	pt1	Constraint point 1 [3]
[in]	pt2	Constraint point 2 [3]
[in]	wt1	Weight for constraint point 1
[in]	wt2	Weight for constraint point 2
[out]	ierr	Error flag

◆ cad_surf_norm()

subroutine cad_surf_norm	(	class(cad_surf), intent(in)	self,
		real(r8), dimension(3), intent(out)	norm,
		real(r8), intent(in)	u,
		real(r8), intent(in)	v
	)

private

Compute unit normal vector for a CAD surface at a specified position.

Parameters

[out]	norm	Surface normal unit vector [3]
[in]	u	Parametric coordinate 1
[in]	v	Parametric coordinate 2

◆ cad_surf_reflect()

subroutine cad_surf_reflect	(	class(cad_surf), intent(in)	self,
		class(cad_surf), intent(out)	copy,
		real(r8), intent(in)	tol,
		integer(i4), intent(in)	k
	)

private

Reflect a surface object across a given plane.

Parameters

[in]	self	Source surface to copy
[out]	copy	Reflected copy of the source surface
[in]	tol	Minimum distance from plane
[in]	k	Coordinate index for the reflection plane

◆ cad_vertex_eval()

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

private

Map parametric possition of a vertex to physical coordinates.

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

[out] pt Position vector [3]

[in] u Parametric coordinate 1 (ignored)

[in] v Parametric coordinate 2 (ignored)

◆ cad_vertex_find()

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

private

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

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

[in] pt Position vector [3]

[out] u Parametric coordinate 1 (ignored)

[out] v Parametric coordinate 2 (ignored)

◆ cad_vertex_reflect()

subroutine cad_vertex_reflect	(	class(cad_vertex), intent(in)	self,
		class(cad_vertex), intent(out)	copy,
		real(r8), intent(in)	tol,
		integer(i4), intent(in)	k
	)

private

Reflect a vertex object across a given plane.

Parameters

[in]	self	Source object to copy
[out]	copy	Reflected copy of the source vertex
[in]	tol	Minimum distance from plane
[in]	k	Coordinate index for the reflection plane

Variable Documentation

◆ active_curve

class(cad_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_surf

class(cad_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.

◆ cad_ngrid

integer(i4), parameter cad_ngrid = 20

Number of grid points to use for object meshes.

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

Detailed Description

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ bernstein()

◆ cad_cmid_error()

◆ cad_curve_cast()

◆ cad_curve_eval()

◆ cad_curve_find()

◆ cad_curve_grid()

◆ cad_curve_midpoint()

◆ cad_curve_reflect()

◆ cad_curve_tang()

◆ cad_scenter_error()

◆ cad_smid_error()

◆ cad_surf_cast()

◆ cad_surf_center()

◆ cad_surf_eval()

◆ cad_surf_find()

◆ cad_surf_grid()

◆ cad_surf_midpoint()

◆ cad_surf_norm()

◆ cad_surf_reflect()

◆ cad_vertex_eval()

◆ cad_vertex_find()

◆ cad_vertex_reflect()

Variable Documentation

◆ active_curve

◆ active_endpts

◆ active_surf

◆ active_wts

◆ cad_ngrid