We find that the topologies of all three surface types can be computed in O(m) time, and that the topology of one surface can be transformed to the topology of another in O(m) time, both in the worst case, where m represents the number of simplexes on the boundary of a β-shape.
Specifically, the vector of surface points can be computed by left-multiplying the vector of control points by a sparse subdivision matrix.
Least-cost path analysis (LCPA) allows designers to find the "cheapest" way to connect two locations within a cost surface, which can be computed by combining multiple criteria, and therefore by accounting for different issues (environmental impact, economic investment, etc).
From the zeta potential, the surface potential can be computed, based on the electrical double layer [23, 24] σ = − 8 ε 0 ε r c R g T sinh F Zζ 2 RT (13).
The reference kinetic energy flux P ref v that is incident on the surface of the wind turbine rotor surface S rotor can be computed as P ref v = 1 2 ρ air S rotor v 3, (2 where ρ air is the air density.
Finally, the ratio of theoretical surface and bulk resistance can be computed in Eq. (3).
By solving both primal and adjoint equation system, the desired (volume-normalised) topological and (surface-normalised) shape sensitivities can be computed as ∂ J ∂ α = u ⋅ v and ∂ J ∂ β = − ν ∂ n u ⋅ ∂ n v, (9).
As a result, the surface temperatures of each component can be computed accurately.
Lastly, the surface crack fracture toughness, KIe, can be computed from JIC based on the fracture mechanics method.
If and are in different positions on the sphere (Figure 11(a)), is the shortest surface distance on the sphere, which can be computed by.
