All examples are implemented in the clawpack software package and full source code is available on the web, along with MATLAB routines for the various mappings. The cubed sphere (Ronchi et al, 1996), which constitutes a spherical surface with six nonoverlapping components, is another overset grid used for the numerical. Pattern formation from a reaction-diffusion equation on the sphere is also considered. An accurate, effcient and scalable cubed-sphere grid framework is described for simu- lation of magnetohydrodynamic (MHD) space-physics flows in domains. Numerical test calculations illustrate the potential use of these grids for a variety of applications including Euler equations, shallow water equations, and acoustics in a heterogeneous medium. Since the ratio between the largest and smallest grids is below 2 for most of our grid mappings, explicit finite volume methods such as the wave-propagation algorithm do not suffer from the center or pole singularities that arise with polar or latitude-longitude grids. Although these grids are highly nonorthogonal, we show that the high-resolution wave-propagation algorithm implemented in clawpack can be used effectively to approximate hyperbolic problems on these grids. A more general domain with a smooth boundary can be gridded by composing one of the mappings from this paper with another smooth mapping from the circle or sphere to the desired domain. Compared to alternative approaches based on a multiblock data structure or unstructured triangulations, this approach simplifies the implementation of numerical methods and the use of adaptive refinement. The grids are logically rectangular and the computational domain is a single Cartesian grid. I will also kick this back to at this point for his opinion on either UV to world space or when to ray cast since he would also be a great source for guidance here.We describe a class of logically rectangular quadrilateral and hexahedral grids for solving PDEs in circular and spherical domains, including grid mappings for the circle, the surface of the sphere, and the three-dimensional ball. Like other electrostatic lenses the gridded lens is not free of spherical aberrations caused primarily by different focusing properties of the electric field. In each scenario, you would need a slightly different method of when to ray cast or if you should set up the entire board first or ray cast as needed. Depending on how you want the UX to feel, it could diverge down a couple of paths like showing the user a legal position for a move by ghosting in a piece as they mouse over an intersection or not showing them anything until they click to place. You could simply do this when the player tries to place a piece and cast a along the vector toward the nearest intersection world position and then pick the collided mesh and return the normal at that point. You would then need the normal from the mesh at that world position, which you may need to do a ray cast to get. This is in C#, but you should be able to convert easily to js/ts since it’s pretty straightforward. Eps 10 vector illustration of 3D Wire-frame, gridded spheres set Stock vector 68190849 Download from Depositphotos Millions of royalty-free vector. Then you need to convert that UV coordinate to a world coordinate using something akin to How to convert pixel/UV coordinates to World Space? - Unity Answers. A gridded sphere is used to show:1) the seismic stations don't need to be lined up longitudinally to create travel-time curves, as they appear in the first animation, and2) a single station records widely separated earthquakes that plot on the travel-time curves. Since you know the interval of the number of squares in UV space, you can figure out the UV position of every intersection quite easily. In that sense, if you are using the shader to set the number of squares, then you will likely need to convert UV space to world space. If you truly need to dynamically change the number of intersections available, then the DCC route won’t be feasible unless you want to make one mesh for each potential configuration. An example above is the cubed-sphere of Figure 3, which is defined by six grid tiles, on which a data field may be represented by several arrays, one per tile. Then you simply need to make the placed piece a child of the appropriate null transform and the position and rotation should be taken care of. The null transform is a position, scale, and rotation so it can hold a direction that points along the normal of the surface. If this is a game board that is always the same (I believe a goban has specific dimensions and number of intersections, but I may be wrong) then the easiest solve is to create your sphere in a DCC tool (blender for example) with null transforms (called empty in Blender) placed in every legal position around your sphere. There are a few ways to do this, but you will need to determine which trade offs are most important to you.
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