Fundamentals - Preventive Biomechanics - page 119

Objective function evaluation at vertex e.

Case distinction
If U ð e Þ \U ð p B Þ replace p W with e, otherwise replace p W with r. In either case
proceed with step 9
Equation ( 3.375 ) can be written in matrix notation using ( 3.372 ) and ( 3.374 ).

6. Step: Partial outside contraction of the simplex Dp B p G r to generate the
potentially new triangle Dp B p G c 2 (cf. Fig. 3 .27 c) by determining the c oor-
dinates of point c 2 through shifting of r along mr about the distance of 0 : 5 mr.

c 2 ¼ m þ m p W
2
¼ 3 ð p B þ p G Þ 2p W
4
¼ 0 : 5 ð m þ r Þ

ð 3 : 376 Þ

Objective function evaluation at vertex c 2 .
Case distinction
If U ð c 2 Þ U ð r Þ replace p W with c 2 and go to step 9, otherwise go to step 8.
Equation ( 3.376 ) can be written in matrix notation using ( 3.372 ) and ( 3.374 ).

7. Step: Partial inside contraction of the simplex Dp B p G r to generate the
potentially new triangle Dp B c 1 p G (cf. Fig. 3.2 7 c) by determining the c oor -
dinates of point c 1 through shifting of r along mr about the distance of mr.
c 1 ¼ p W þ m p W
2
¼ p B þ p G þ 2p W
4
¼ 0 : 5 ð m þ p W Þ

ð 3 : 377 Þ

Objective function evaluation at vertex c 1 .
Case distinction
If U ð c 1 Þ p W replace p W with c 1 and go to step 9.
Equation ( 3.377 ) can be written in matrix notation using ( 3.372 ).

8. Step: Total contraction (shrinking) of the simplex Dp B p W p G towards p B to
generate the potentially new triangle Dp B p W p G by deter minin g the coordi-
nates of points p W and p G thro ugh sh ifting o f p W along p W p B and p G along
p G p B about the distance of 0 : 5 p W p B and 0 : 5 p G p B , respectively.
p W ¼ p B þ p W p G ¼ p B þ p G and ð 3 : 378 Þ

2 2