File size: 1,825 Bytes
785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | import OAI.Geometry.CylinderCovering.Singular.EdgeOneDefinitions
import OAI.Geometry.RuledCovering.Model
namespace OAI
noncomputable section
namespace SingularEdgeOne
def edgeDomain0 : Set RuledApproximation.Plane :=
{z | 0 ≤ z 1 ∧ z 1 ≤ (1 / 2 : ℝ) ∧ |z 0| ≤ z 1 / 2}
def edgeField (p : ℝ) (z : RuledApproximation.Plane) : RuledApproximation.Plane :=
RuledApproximation.vec2 (edgeU p (z 0) (z 1)) (edgeV p (z 0) (z 1))
def physicalSimilarity (z : RuledApproximation.Space) : RuledApproximation.Space :=
RuledApproximation.vec3 (z 1 / 2) (z 0 / 2) (z 2 / 2)
def labelMap (z : RuledApproximation.Plane) : RuledApproximation.Plane :=
RuledApproximation.vec2 (z 0 / 2) (z 1)
def edgeTetrahedron : Set RuledApproximation.Space :=
{z | ∃ s : ℝ, 0 ≤ s ∧ s ≤ 1 ∧ |z 0| ≤ s / 2 ∧ |z 1| ≤ (1 - s) / 2 ∧
z 2 = (1 / Real.sqrt 2) * s}
def edgeLower (p k : ℝ) (D : Set RuledApproximation.Plane) : Set RuledApproximation.Space :=
{z | ∃ b ∈ D, ∃ y : ℝ, |y| ≤ (1 / 2 : ℝ) ∧
z = RuledApproximation.vec3 (b 0 + k * y * edgeU p (b 0) (b 1)) y
((1 / Real.sqrt 2) * (b 1 + k * y * edgeV p (b 0) (b 1)))}
def edgeUpper (p k : ℝ) (D : Set RuledApproximation.Plane) : Set RuledApproximation.Space :=
{z | ∃ b ∈ D, ∃ x : ℝ, |x| ≤ (1 / 2 : ℝ) ∧
z = RuledApproximation.vec3 x (b 0 - k * x * edgeU p (b 0) (b 1))
((1 / Real.sqrt 2) * (1 - (b 1 - k * x * edgeV p (b 0) (b 1))))}
def upperSegments (p c : ℝ) (D : Set RuledApproximation.Plane) : Set RuledApproximation.Space :=
{z | ∃ b ∈ D, ∃ y : ℝ, |y| ≤ 1 ∧
z = RuledApproximation.vec3
(b 0 - c * y * RuledApproximation.singularField p b 0) y
(Real.sqrt 2 * (1 - (b 1 - c * y * RuledApproximation.singularField p b 1)))}
end SingularEdgeOne
end
end OAI
|