surface_branch_glue.cpp File Reference

Mirroring & gluing surfaces together. More...

Go to the source code of this file.

Detailed Description

Mirroring & gluing surfaces together.

Author

Mitch Richling http://www.mitchr.me/

Date

2024-07-16

Standards

C++23

Copyright

Copyright (c) 2024, Mitchell Jay Richling http://www.mitchr.me/ All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Details

In surface_plot_edge.cpp we encountered the unit sphere defined by the zeros of \(1^2=x^2+y^2+z^2\), and the related function \(f(x,y)=\sqrt{1-x^2-y^2}\) obtained by "solving" for \(z\). Note that if \(z=f(x, y)\), then both \(z\) and \(-z\) satisfy the original equation. While the square root function is positive by definition, we might wish to think of \(f(x, y)\) as a multi-valued function with two branches – a positive one and a negative one.

In simple cases like this, where the two branches are reflections across an axis plane, we can use MR_cell_cplx::mirror() to mirror the geometry and seal up any holes. This is really the only change from surface_plot_edge.cpp.

Definition in file surface_branch_glue.cpp.