mirrors/hyperrogue
1
0
Fork 0
mirror of https://github.com/zenorogue/hyperrogue.git synced 2024-12-26 01:50:36 +00:00
Code Issues Releases Wiki Activity

nil Christoffel formulas in model

Browse Source
This commit is contained in:
Zeno Rogue 2023-08-07 20:46:45 +02:00
parent 097ded1bd0
commit d2c601834a
1 changed files with 26 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

26
nonisotropic.cpp
View File

@ -787,6 +787,32 @@ EX namespace nilv {
hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported, ld model = model_used) {
/* to do: write these formulas in model */
if(model == nmSym) {
hyperpoint c; c[3] = 0;
ld x = Position[0]; ld y = Position[1]; ld diag = (y*y-x*x)/8;
c[ 0 ] = 0
+ Velocity[ 0 ] * Transported[ 1 ] * ( -y/4 )
+ Velocity[ 1 ] * Transported[ 0 ] * ( -y/4 )
+ Velocity[ 1 ] * Transported[ 1 ] * ( x/2 )
+ Velocity[ 1 ] * Transported[ 2 ] * ( -1/2. )
+ Velocity[ 2 ] * Transported[ 1 ] * ( -1/2. );
c[ 1 ] = 0
+ Velocity[ 0 ] * Transported[ 0 ] * ( y/2 )
+ Velocity[ 0 ] * Transported[ 1 ] * ( -x/4 )
+ Velocity[ 0 ] * Transported[ 2 ] * ( 1/2. )
+ Velocity[ 1 ] * Transported[ 0 ] * ( -x/4 )
+ Velocity[ 2 ] * Transported[ 0 ] * ( 1/2. );
c[ 2 ] = 0
+ Velocity[ 0 ] * Transported[ 0 ] * ( x*y/4 )
+ Velocity[ 0 ] * Transported[ 1 ] * diag
+ Velocity[ 0 ] * Transported[ 2 ] * ( x/4 )
+ Velocity[ 1 ] * Transported[ 0 ] * diag
+ Velocity[ 1 ] * Transported[ 1 ] * ( -x*y/4 )
+ Velocity[ 1 ] * Transported[ 2 ] * ( y/4 )
+ Velocity[ 2 ] * Transported[ 0 ] * ( x/4 )
+ Velocity[ 2 ] * Transported[ 1 ] * ( y/4 );
return c;
}
if(model == nmHeis) {
ld x = Position[0];
return point3(