Triangulation of Polyhedral Surfaces

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2015-11-14 20:18

This example demonstrates the triangulation of polyhedral surfaces, illustrating the process of constructing triangular meshes. Key math concepts include polygons, solid geometry, trigonometry, and complex number operations. Construction highlights from the GeoGebra command summary involve commands like If, Length, Sequence, Sum, Div, Element, TableText, and objects such as mm5d, mm5, mm5a, etc. It is suitable for high school and above students to understand discretization representation and computational methods for complex geometric shapes.

GeoGebra Commands & Parameters

If(bu0, A00, A00d) → A00_0
Length(A00_0) → n
Length(l2) → läl2
Sequence(sgn(Determinant[{Element[A00_0, i1] - Element[A00_0, j], Element[A00_0, i2] - Element[A00_0, j], Element[A00_0, i3] - Element[A00_0, j]}]), j, 1, n) → l01
If((Length[KeepIf[x > 0, l01]] * Length[KeepIf[x < 0, l01]]) ≠ 0, -7, 7) → a7
Length(A00d) → zzz
Sequence(Sum[Zip[Element[A, k], A, R01]], k, 1, Length[Element[R01, 1]]) → R02
Sum(Zip[(T * F), T, SysTimeAkt1, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs1
Sum(Zip[(T * F), T, SysTimeAkt2, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs2
Div(TimeRelab, 3600) → H
Div(TimeRelab - (H * 3600), 60) → M
Element(ZwZeit, step) → text10
TableText({Append["Polyhedron: N=", {Length[A00]}], Append["r=", {r}], Append["n-cornered \;figure: n=", mm5a], Append["their\; numbers: N_n=", mm7a], Append["Volume: V=", {Vol_r}]}, "hr ") → text7
TableText({Append["Dual: N=", {Length[A00d]}], Append["r=", {r_d}], Append["n-cornered \;figure: n=", mm5ad], Append["their\; numbers: N_n=", mm7ad], Append["Volume: V=", {Vold_r}]}, "hr ") → text20
TableText({Append["a duration", Last[ZwZeit, Min[10, Length[ZwZeit]]]]}, "v") → text2c
Length(A00) → lm1
Element(A00, 32) → m11