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Geometry:

  • P = 8mm

  • Width of brick: 15.8mm

  • Length of brick: 31.8mm

  • Stud: 4.8mm

  • Stud to side: 3.9mm

  • Maximum angle for a turn point is thus A = acrcos(6.3/8) = 0.664054277 radians (38.0475075 degrees).

Maximal angle steps based on number of brick of models on each side of the turn point:

Simple formulas for an isosceles triangle implies the bound A on the angle that can be allowed given the distance d (in mm):

sin(A/2)*d < 0.1/2 => A < asin(1/20/d)*2

  • Size 1: Max distance: d=sqrt(12^2+28^2)=30.46mm. Max angle: a<asin(1/20/d)2=0.0032826623 radians. Steps: A/a < 203 => 2203+1=407 steps in total.

  • Size 2: Max distance: d=sqrt(20^2+52^2)=55.71mm. Max angle: a<asin(1/20/d)2=0.00179489564 radians. Steps: A/a < 370 => 2370+1=741 steps in total.

  • Size 3: Max distance: d=sqrt(28^2+76^2)=80.99mm. Max angle: a<asin(1/20/d)2=0.00123466207 radians. Steps: A/a < 538 => 2538+1=1077 steps in total.

Optimizations

The times (in seconds) of this section are measured by finding models with the program running in debug mode. "i7" and "i5" refer to test machines. "i7" is a Lenovo Thinkpad T440p from 2014 while "i5" is a Sony Vaio VPCEB4X1E from 2011 running in low performance power saving mode.

Different tests are used to give insight into the performance improvements of the various optimizations.

Test with 3 bricks

Configuration consisting of 3 bricks

The following improvements are for finding all models with 3 bricks. Notice that no models are actually found in this test.

Optimization i7 i5
None 180 -
Replacing diagonal union-find merging with angle locking 153 212
Compute indices for SML-mapping dynamically - 202
Compute configuration for SML-mapping dynamically - 199
Precompute bricks that might intersect SML-mapping - 96
Don't consider connecting brick to be intersectable - 62
Split handling of the SML sets and detect early if a model is impossible - 50
Special handling for models with turning single brick SCCs (TSB) at the end of model: Speed up when angle is free 6 11
Modify the SML-result set to accomodate intervals from TSBs 2 3
Run using release-build 0 1

Further details

To be added.