Slope Map on Terrains
I previously shared the Grasshopper definition for terrain generation that we used in last year’s Basic Design studio. One of the goals of this project was to take the first step toward developing students’ skills in understanding, processing, and utilizing terrain data as a design input. To support this objective, we provided them with small supplementary tools. One of these tools was the slope map. As you can see, this is quite a simple Grasshopper definition. It computes the slope of a given surface. To do this, we calculate the dot product of the surface normal vectors at evaluated points and the World-Z vector. For the given dimensions, this value ranges roughly between 90 and 100 and is visualized using colored dots. You may need to recalibrate these values when analyzing your own surfaces. On this occasion, it is worth recalling what the dot product actually is. According to Khan Academy:
The dot product is a fundamental way we can combine two vectors. Intuitively, it tells us something about how much two vectors point in the same direction.
If you recall, this was also a calculation I explored using Python in my Design Mathematics course. You can find the dot product explanation and Rhino Python implementation here. Particularly when learning mathematics and geometry, we often wonder how this knowledge will be useful to us. Truth be told, not every piece of knowledge has to serve an immediate practical purpose. Yet, as you can see, some of it genuinely does. Returning to our terrain model, you can download the Grasshopper definition below. For the animation, I stepped the SEED values in the Terrain Generator code between 6.0 and 6.2.
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