Rodney

In Week 0 the Harvard CS50 course demos programming using the learning tool called 'Scratch'. The first intro course I took in programming used 'Alice'. I liked Alice because it could load OBJ models and Animation:Master could output OBJ models! Scratch is more popular and used more often and its likely if you are younger than 30 you've been exposed to it if you had any computer related classes in school. In Week 1 the course move on to using the C language. This being quite useful as C++ derives much of its standard usage from C. And C++ is what drives programs like Animation:Master.

Here's your chance to master the art of programming and computer science. The course is starting today (officially) but has been ran continuously for the past few years. The course is self paced. Link: https://www.edx.org/learn/computer-science/harvard-university-cs50-s-introduction-to-computer-science Take the plunge. You know you want to. You know you need to.

My current take on this gap between bipartite grids and four color theory is that at the moment we join 'areas' (grid squares) we need to establish a new 'color'. According to the science we don't need more than 4 colors but we can have as many colors as we want. So... Underlying the whole gamut of shape and group assignments our algoritm can chug away at reducing to 4 colors. We then dictate in some fashion the shapes and extents of those areas and build upon and extrapolate from that. To the observant this might appear to place us at the intersection between raster and vector graphics. Attached is this 'nonbipartite' grid project: nonbipartite.prj

Here's an example of a non-bipartite grid, meaning that no two grid squares of the same color touch (even at the corners). If they could touch at the corners they could be termed 'bipartite'. In A:M we can work around this by having multiple groups of the same color. In effect, masking or hiding what is actually happening. In other words, presenting a grid that appears bipartite when in fact it is not. Something worth observing here might be that initial choice of what grid squares were white (given that underneath it all all the grid squares are black). In the first row our white group has started with the second patch. In the second row we shift and choose the patch to the left. We could have just as easily chose to shift right and add that to our group instead. There is something of significance in this choice as it sets the stage for what other grid squares can be selected and included in our group and what grid squares must be left out. But we must make a choice... so is one choice more correct than the other? Should we turn left or turn right? As with continuity it would at least intially appear that consistency is key. Our decision being made we must proceed and deal with the consequences.

If A:M were autogrouping I'm curious how it would color these areas of continuity. Especially as A:M's named groups can consist of areas also covered by other named groups. Four color theory would suggest we need a minimum of 4 colors to assign a unique color to every patch and have no two patches adjacent to each other be the same color. If the surface is a grid... we can get away with only 2 colors (ala checkerboard). But our models rarerly fit into a perfect grid. And discontinuity leads to many problems... In fact, I'd say it runs smack dab into the 4 color theory problem but in this particular case (that of grids (read: patches) thinking we can eternally steer clear of being represented with a less than 4 control points/colors. Added: Here we likely need to look into 'strongly colored grids' or 'king's grids' where no two grid squares of the same color can touch each other. If they do touch then that creates a cascading effect where other grid squares also must change color/grouping. In A:M we see this when we attempt to group patches and inadvertently have other patches join our group becuase they share those other area's control points

One of the (many) plusses of spline continuity is how we can use processes such as 'splitpatch' and autobeveling to increase or potentially decrease the density of our meshes. We do have to watch out for those extraordinary vertexes... er... patches. We don't control all the processes so we have to consider closely how those processes deal with discontinuity (whether preceived or actual).

This intermediary outline (ala lofting*) has a few advantages. One of those is how it avoids creating internal patches. *I rarely here the term 'lofting' anymore. Extrusion seems to have displaced the term almost entirely. I had to think hard just to remember the term and that old A:M plugin A:M Loft.

At this point we should note that there are other ways we can resolve this crisis of continuity. For instance rather than connect edges prior to extrusion into depth we might add a contour of our surface inbetween that surface and its other side. This middleman approach can be used if the surface has continuity at its corners or not but here I show it with the surface with corner continuity:

Moving too quickly to resolve our model to be all 4 point patches can lead to new issues of continuity: That might be fine... if we able and willing to track those cases of discontinuity. Perhaps, even leverage those outliers as opportunity.

One way we might resolve this is to ensure our outer contour (the edge that will extend in depth) has continuity: Astute observers may notice a simularity with that 'basketball approach to spline coverage. While not a problem for us here, the 3 point patches on the corners should be noted as they are not our ideal. This assuming an ideal patch consists of four points which is something we have not yet proven to be the optimal case but for now can take that on faith. We might step past this potential obstacle by bisecting those three point patches and adding the 4th control point but that might not be optimal for viewing peaked models:

Splines and Patches have (thankfully) some unique characteristics. However, as has long been experienced, this presents some unique challenges in a world that doesn't deal well with continuity. I'm attaching two versions of the same model... one is just peaked while the other not-peaked. In the peaked version we might not see the problem as it is hidden from our view. The corner looks like a single line/spline connecting two copies of the same surface, slightly offset from each other. If we unpeak this model we can see the problem: We have continuity but that continuity leaves a gap (a leak so to speak) in our collection of surfaces. Aside: It's fine to have gaps but we want to be able to know exactly where they are and be able to control them) ThicknessAndEndpoints_peaked.mdl ThicknessAndEndpoints.mdl

I guess this might be my take on the ends of boxy or cylindrical shapes: (The basketball splinage approach... although I do sense that we maybe should call it the Malo Method as it allows for interating and increasing/decreasing detail and patch count)

Because this is impossible we must do it. Now all we have to do is live that long.

I feel a bit like I've just woke up in an alternate universe. This has been a thing for a few years now and I'm just now discovering it. (Probably because this is the first time I've used Powerpoint and Word in years) Here's what surely must be Euisung Lee's Running T-Rex of old school A:M fame... obviously repainted... but... ...imported into Powerpoint as an animated model that can be turned around, duplicated and scaled... ...and exported as an animated gif with transparency or an MP4 video. Trexes.mp4 What is a bit disconcerting to me is that Microsoft has shut down/deprecated its Paint 3D program which suggests interest in such 3D isn't actually on the rise but perhaps on just the latest cyclic decline.