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// knotty.fe
// Evolver data for 3,2 torus knot (trefoil) with various knot energies.
// You need to set one type of energy and one type of length constraint;
// see the set_* commands in the "read" section of the datafile.
// Not all combinations are workable.
string // this is a 1D surface
parameter maj_r = 2 // torus major radius
parameter min_r = 0.5 // torus minor radius
boundary 1 parameter 1 // parametric curve around torus
x1: cos(2*p1)*(maj_r + min_r*cos(3*p1))
x2: sin(2*p1)*(maj_r + min_r*cos(3*p1))
x3: min_r*sin(3*p1)
// Here follow six different types of energy. Switch between them
// with the set_* commands in the bottom section of this datafile.
// elastic bending energy, i.e. squared curvature
quantity bending_energy ENERGY modulus 0 method sqcurve_string global
// conducting wire vertex energy
quantity conduct_energy ENERGY modulus 1 method knot_energy global
// insulating wire vertex energy
quantity insul_energy ENERGY modulus 0 method edge_knot_energy global
// Greg Buck's 1/(d1+d2+d3+d4-2(L1+L2)) energy
quantity buck_energy ENERGY modulus 0 method buck_knot_energy global
// have to start with modulus 0 since edges too long at start */
// Greg Buck's normal projection energy
quantity proj_energy ENERGY modulus 0 method proj_knot_energy global
// Peter Doyle's conformal circle energy
quantity circle_energy ENERGY modulus 0 method circle_knot_energy global
// Here follow three ways to control the length of edges.
// Switch between them with the set_* commands below.
// Elastic stretching energy to encourage edges to all have the same length.
// Use "hooke_length := value" command to set hooke_length to desired
// edge length
quantity hooke ENERGY modulus 0 method hooke_energy global
// Individually set edge equilibrium lengths.
// Use "set edge hooke_size expr" to set desired edge lengths
// When used, the modulus needs to be set high, like 1000 or 10000,
// to provide decent stiffness.
define edge attribute hooke_size real
quantity hooke2 ENERGY modulus 0 method hooke2_energy global
// to keep total length fixed
quantity knot_length FIXED = 24 modulus 1 method edge_tension global
vertices
1 0.0*pi boundary 1
2 0.2*pi boundary 1
3 0.4*pi boundary 1
4 0.6*pi boundary 1
5 0.8*pi boundary 1
6 1.0*pi boundary 1
7 1.2*pi boundary 1
8 1.4*pi boundary 1
9 1.6*pi boundary 1
10 1.8*pi boundary 1
edges
1 1 2 boundary 1
2 2 3 boundary 1
3 3 4 boundary 1
4 4 5 boundary 1
5 5 6 boundary 1
6 6 7 boundary 1
7 7 8 boundary 1
8 8 9 boundary 1
9 9 10 boundary 1
10 10 1 boundary 1
read // some initialization commands
r 2 // refining twice produces 40 vertices
unset vertices boundary 1 // release from parametric curve
unset edges boundary 1
set edge tension 0 // get rid of default tension energy
set edge color white where id <= edge_count/2 // dashed coloring
// Set all quantity moduli to zero
zero_moduli := {
bending_energy.modulus := 0;
conduct_energy.modulus := 0;
insul_energy.modulus := 0;
buck_energy.modulus := 0;
proj_energy.modulus := 0;
circle_energy.modulus := 0;
}
// Set up individual types of energy
set_bending := { zero_moduli; bending_energy.modulus := 1; }
set_conduct := { zero_moduli; conduct_energy.modulus := 1; }
set_insul := { zero_moduli; insul_energy.modulus := 1; }
set_buck := { zero_moduli; buck_energy.modulus := 1; }
set_proj := { zero_moduli; proj_energy.modulus := 1; }
set_circle := { zero_moduli; circle_energy.modulus := 1; }
// Set up type of length constraint
hooke_length := total_length/edge_count;
set edge hooke_size total_length/edge_count;
set_length := { fix knot_length; hooke.modulus := 0; hooke2.modulus := 0; }
set_hooke := { unfix knot_length; hooke.modulus := 1000; hooke2.modulus := 0; }
set_hooke2 := { unfix knot_length; hooke.modulus := 0; hooke2.modulus := 1000; }
// Sample evolution
gogo := { g 50; U; g 50; }
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