With the Flat surface option not selected, the surface geometry can be defined either using data points (discussed here) or externally (discussed in the next section). The Data source dropdown in the tire component properties provides three options to define the surface data points: inline, using a file, or using an attachment. In each case, data points are given as a matrix in which the first column and first row represent discrete points on two of the global coordinate axes.
With the inline option, the matrix is entered in the MapleSim GUI. To change the matrix dimensions, rightclick on the text input field and select Edit Matrix Dimensions.
Alternatively, a CSV, XLS, or XLSX file can be used to define the matrix by choosing file or attachment for the Data source parameter and selecting the file or attachment as the Surface data parameter.
The interpretation of the data points matrix depends on the selected vector for direction of gravity, ${\stackrel{\^}{e}}_{g}$, in the Multibody Settings. Different interpretations are summarized below

Gravity parallel to xaxis




Gravity parallel to yaxis




Gravity parallel to zaxis



For the given surface data points, an iterative algorithm calculates the surface normal vector, ${\stackrel{\^}{e}}_{n}$, and tire center distance from the surface, $\mathrm{rz}$
The integer ${n}_{\mathrm{iter}}$ in the properties specifies the number of iterations. The recommended value is from 1 to 5 to get a reasonable tradeoff between accuracy and performance.
To clarify the employed algorithm, the following describes the steps of the algorithm for ${n}_{\mathrm{iter}}\=2$:
1. Iteration 1:
1) Project the tire center point onto the given surface to find ${\stackrel{\&conjugate0;}{p}}_{1}$. This requires interpolation of the provided surface data points. The interpolation smoothness is determined by the smoothness dropdown in the properties, as shown below. We suggest using the cubic splines to interpolate smoothly between the surface data points.
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2) Create a tangent plane to the surface directly below the tire center. The radius of this tangent plane is controlled by the ${\mathrm{\delta}}_{L}$ parameter in the properties.
3) Project the vector from the surface point to the tire center point onto the surface normal vector to get the distance.
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2. Iteration 2a:
1) Replace tire center with an intermediate point, ${\stackrel{\&conjugate0;}{r}}_{2}$.
2) Project ${\stackrel{\&conjugate0;}{r}}_{2}$ onto the given surface to obtain ${\stackrel{\&conjugate0;}{p}}_{2}$. Again, this requires interpolation with smoothness defined by the smoothness dropdown in the properties.
3) Repeat the tangent plane calculation with the vertical projection of this point. Again, the radius of this tangent plane is controlled by ${\mathrm{\delta}}_{L}$.
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3. Iteration 2b:
1) Project the vector from the surface point to the tire center point onto the surface normal vector to get the distance.
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After these steps for ${n}_{\mathrm{iter}}\=2$ are completed, the $\mathrm{n2}$ unit vector shown in the figure above is chosen as the surface normal vector, ${\stackrel{\^}{e}}_{n}$, and ${d}_{2}$ is taken as the tire center distance from the surface, $\mathrm{rz}$.