Parallel Vectors Operator

Namespaces
namespace	tatooine
namespace	tatooine::detail

Functions
template<typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (polymorphic::vectorfield< VReal, 3 > const &vf, polymorphic::vectorfield< WReal, 3 > const &wf, rectilinear_grid< XDomain, YDomain, ZDomain > const &g, TReal const t, execution_policy_tag auto const policy, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (polymorphic::vectorfield< VReal, 3 > const &vf, polymorphic::vectorfield< WReal, 3 > const &wf, rectilinear_grid< XDomain, YDomain, ZDomain > const &g, TReal const t, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, rectilinear_grid< XDomain, YDomain, ZDomain > const &g, TReal const t, execution_policy_tag auto const policy, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, rectilinear_grid< XDomain, YDomain, ZDomain > const &g, TReal const t, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, rectilinear_grid< XDomain, YDomain, ZDomain > const &g, execution_policy_tag auto const policy, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, rectilinear_grid< XDomain, YDomain, ZDomain > const &g, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, linspace< XReal > const &x, linspace< YReal > const &y, linspace< ZReal > const &z, TReal const t, execution_policy_tag auto const policy, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, linspace< XReal > const &x, linspace< YReal > const &y, linspace< ZReal > const &z, TReal const t, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, linspace< XReal > const &x, linspace< YReal > const &y, linspace< ZReal > const &z, execution_policy_tag auto const policy, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (vectorfield< V, VReal, 3 > const &vf, vectorfield< W, WReal, 3 > const &wf, linspace< XReal > const &x, linspace< YReal > const &y, linspace< ZReal > const &z, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename VReal , typename VIndexing , typename WReal , typename WIndexing , typename AABBReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (dynamic_multidim_array< vec< VReal, 3 >, VIndexing > const &vf, dynamic_multidim_array< vec< WReal, 3 >, WIndexing > const &wf, axis_aligned_bounding_box< AABBReal, 3 > const &bb, execution_policy_tag auto const policy, Preds &&... preds)
	This is an implementation of [5]. More...
template<typename VReal , typename VIndexing , typename WReal , typename WIndexing , typename AABBReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>
auto	tatooine::parallel_vectors (dynamic_multidim_array< vec< VReal, 3 >, VIndexing > const &vf, dynamic_multidim_array< vec< WReal, 3 >, WIndexing > const &wf, axis_aligned_bounding_box< AABBReal, 3 > const &bb, Preds &&... preds)
	This is an implementation of [5]. More...

Detailed Description

Cube Setup

A cube's vertices are numbered like this where

• 0 -> 1 corresponds to x-direction,
• 0 -> 2 corresponds to y-direction and
• 0 -> 4 corresponds to z-direction.

   6---------7
  /.        /|
 / .       / |
2---------3  |
|  4. . . |. 5
| .       | /
|.        |/
0---------1

A cube can be decomposed into 5 tetrahedrons in 2 ways. The first one is called 'non-turned' and the other one is called 'turned'.

Tetrahedrons per cube

The tetrahedrons are setup like this:

• turned tetrahedrons per cube:
  • [0]: 0236 (with triangles 023, 026, 036, 236)
  • [1]: 0135 (with triangles 013, 015, 035, 135)
  • [2]: 3567 (with triangles 356, 357, 367, 567)
  • [3]: 0456 (with triangles 045, 046, 056, 456)
  • [4]: 0356 (with triangles 035, 036, 056, 356)
• non-turned tetrahedrons per cube:
  • [0]: 0124 (with triangles 012, 014, 024, 124)
  • [1]: 1457 (with triangles 145, 147, 157, 457)
  • [2]: 2467 (with triangles 246, 247, 267, 467)
  • [3]: 1237 (with triangles 123, 127, 137, 237)
  • [4]: 1247 (with triangles 124, 127, 147, 247)

Faces with constant x

• turned inner tet order:
  • [0]: 046 / 157
  • [1]: 026 / 137
• non-turned inner tet order:
  • [0]: 024 / 135
  • [1]: 246 / 357

Faces with constant y

• turned inner tet order:
  • [0]: 015 / 237
  • [1]: 045 / 267
• non-turned inner tet order:
  • [0]: 014 / 236
  • [1]: 145 / 367

Faces with constant z

• turned inner tet order:
  • [0]: 013 / 457
  • [1]: 023 / 467
• non-turned inner tet order:
  • [0]: 012 / 456
  • [1]: 123 / 567

Faces with constant z

• turned inner tet order:
  • [0]: 035
  • [1]: 036
  • [2]: 356
  • [3]: 056
• non-turned inner tet order:
  • [0]: 124
  • [1]: 127
  • [2]: 147
  • [3]: 247

Function Documentation

parallel_vectors() [1/12]

template<typename VReal , typename VIndexing , typename WReal , typename WIndexing , typename AABBReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	dynamic_multidim_array< vec< VReal, 3 >, VIndexing > const &	vf,
		dynamic_multidim_array< vec< WReal, 3 >, WIndexing > const &	wf,
		axis_aligned_bounding_box< AABBReal, 3 > const &	bb,
		execution_policy_tag auto const	policy,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [2/12]

template<typename VReal , typename VIndexing , typename WReal , typename WIndexing , typename AABBReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	dynamic_multidim_array< vec< VReal, 3 >, VIndexing > const &	vf,
		dynamic_multidim_array< vec< WReal, 3 >, WIndexing > const &	wf,
		axis_aligned_bounding_box< AABBReal, 3 > const &	bb,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [3/12]

template<typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	polymorphic::vectorfield< VReal, 3 > const &	vf,
		polymorphic::vectorfield< WReal, 3 > const &	wf,
		rectilinear_grid< XDomain, YDomain, ZDomain > const &	g,
		TReal const	t,
		execution_policy_tag auto const	policy,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [4/12]

template<typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	polymorphic::vectorfield< VReal, 3 > const &	vf,
		polymorphic::vectorfield< WReal, 3 > const &	wf,
		rectilinear_grid< XDomain, YDomain, ZDomain > const &	g,
		TReal const	t,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [5/12]

template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		linspace< XReal > const &	x,
		linspace< YReal > const &	y,
		linspace< ZReal > const &	z,
		execution_policy_tag auto const	policy,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [6/12]

template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		linspace< XReal > const &	x,
		linspace< YReal > const &	y,
		linspace< ZReal > const &	z,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [7/12]

template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		linspace< XReal > const &	x,
		linspace< YReal > const &	y,
		linspace< ZReal > const &	z,
		TReal const	t,
		execution_policy_tag auto const	policy,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [8/12]

template<typename V , typename W , typename VReal , typename WReal , typename XReal , typename YReal , typename ZReal , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		linspace< XReal > const &	x,
		linspace< YReal > const &	y,
		linspace< ZReal > const &	z,
		TReal const	t,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [9/12]

template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		rectilinear_grid< XDomain, YDomain, ZDomain > const &	g,
		execution_policy_tag auto const	policy,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [10/12]

template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		rectilinear_grid< XDomain, YDomain, ZDomain > const &	g,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [11/12]

template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		rectilinear_grid< XDomain, YDomain, ZDomain > const &	g,
		TReal const	t,
		execution_policy_tag auto const	policy,
		Preds &&...	preds
	)

This is an implementation of [5].

parallel_vectors() [12/12]

template<typename V , typename W , typename VReal , typename WReal , typename XDomain , typename YDomain , typename ZDomain , arithmetic TReal, invocable< vec< common_type< VReal, WReal >, 3 > >... Preds>

auto tatooine::parallel_vectors	(	vectorfield< V, VReal, 3 > const &	vf,
		vectorfield< W, WReal, 3 > const &	wf,
		rectilinear_grid< XDomain, YDomain, ZDomain > const &	g,
		TReal const	t,
		Preds &&...	preds
	)

This is an implementation of [5].