Posted here are some examples of the visual output possible with mesh vertex coloring in Rhino’sGrasshopper plugin. This is an evolution of a previous definition which was posted that calculates sun angles at surface subdivision points. A mesh was created based on the surface subdivision. The data from each of the points was then sorted and passed onto the mesh verticies as color information. Here are examples of six different data streams

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Posted here are some examples of the visual output possible with mesh vertex coloring in Rhino’s Grasshopper plugin. This is an evolution of a previous definition which was posted that calculates sun angles at surface subdivision points. A mesh was created based on the surface subdivision. The data from each of the points was then sorted and passed onto the mesh verticies as color information. Here are examples of six different data streams

**Sun Angle Calculation:**

This data set takes the angle from a sample sun path at each subdivision point. Animation shows the sample sun path through a regular cycle. An attempt was made to simulate the shadow by intersecting a line from the sample sun path through a reference plane and generating a surface from the resulting points.

**Point Distance:**

This data set calculates the distance from an attractor point to all the subdivision points on a surface.

**Gaussian Curvature:**

[From Wikipedia]

In differential geometry, the **Gaussian curvature** or **Gauss curvature** of a point on a surface is the product of the principal curvatures, *κ*_{1} and *κ*_{2}, of the given point. It is an *intrinsic* measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is embedded in space. This result is the content of Gauss’s Theorema egregium.

WOLFRAM MATHWORLD: Gaussian Curvature

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**Mean Curvature:**

[From Wikipedia]

In mathematics, the **mean curvature** *H* of a surface *S* is an *extrinsic* measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space.

The concept was introduced by Sophie Germain in her work on elasticity theory. ^{[1]}^{[2]}

WOLFRAM MATHWORLD: Mean Curvature

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**Principal Curvature:**

[MINIMUM]

[From Wikipedia]

In differential geometry, the two **principal curvatures** at a given point of a surface measure how the surface bends by different amounts in different directions at that point.

At each point *p* of a differentiable surface in 3-dimensional Euclidean space one may choose a unit normal vector. A normal plane at *p* is one that contains the normal, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve. This curve will in general have different curvatures for different normal planes at *p*. The **principal curvatures** at *p*, denoted *k*_{1} and *k*_{2}, are the maximum and minimum values of this curvature.

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**Principal Curvature:**

[MAXIMUM]

WOLFRAM MATHWORLD: Principal Curvatures

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The work in this definition has been a collaboration between CarloMaria Ciampoli and Luis E. Fraguada.