Data Landscapes 3

Parametric Variations

The topic of this section is to develop an approach for methodically documenting the variations produced by parametric models. If we consider each model parameter as a dimension, their combinations define a space of all possible outcomes. A parametric model thus defines a family of designs driven by a set of parameters which result to specific design instances.

The challenge is in presenting a high-level view of the systemic behaviour of the design model and the effects of parameter interactions to design outcomes. Mapping variations is aimed at assisting exploration of design possibilities as well as providing evidence-based support for decision making i.e. selecting one of the potentially infinite options using rational thinking.

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A common approach for documenting multi-dimensional models is using variation maps: tables that display the design outcomes of varying two parameters at a time. The model above illustrates a scalar field surface driven by three parameters “t”, “s”, and “c”. The ranges for each parameter are carefully set using the slider options to the following boundaries “t: [0, 16]”, “s: [0, 6]” and “c: [0, 10]”.

To visualize interactions between parameters and present a comprehensive view of the design space we need to produce all pairwise combinations: “t|s”, “s|c” and “c|t” as variation maps seen below. Note that we keep the view orientation constant so the result can be compared visually in the same manner

t|s	0	3	6
0	[0,0,5] A=961, H=0	[0,3,5] A=1221, H=6	[0,6,5] A=1731, H=12
8	[8,0,5] A=961, H=0	[8,3,5] A=1154, H=6	[8,6,5] A=1553, H=12
16	[16,0,5] A=961, H=0	[16,3,5] A=1133, H=6	[16,6,5] A=1497, H=12

Notice that we use only three spot values, low, middle and high, for each parameter i.e. “t: {0, 8, 16}”, “s: {0, 3, 6}” and “c: {0, 5, 10}”. If the effects of varying a parameter are not clear by looking at a row or a column at a time, we may need additional interim value steps e.g. 4 or 5. Of course theoretically the larger the table the better but as the size of options increases quadratically to the number of values, i.e. for “n” values we need “n2” cells, we need to balance between comprehension and effort.

s|c	0	5	10
0	[0,0,0] A=961 H=0	[0,0,5] A=961 H=0	[0,0,10] A=961 H=0
3	[0,3,0] A=961 H=0	[0,3,5] A=1221 H=6	[0,3,10] A=1731 H=6
6	[0,6,0] A=961 H=0	[0,6,5] A=1731 H=12	[0,6,10] A=2932 H=12

As we are varying two parameters for each map, we need to fix all other parameters values. Here we have only one non-varying parameter assigned with a value seen in the caption of each table. The value chosen for held-constant parameters is either its minimum, maximum or middle value, based on which seems more reasonable. The important point is to keep the value fixed across all variations presented in a table

c|t	0	8	16
0	[0,3,0] A=961 H=0	[8,3,0] A=961 H=0	[16,3,0] A=961 H=0
5	[0,3,5] A=1221 H=6	[8,3,5] A=1154 H=6	[16,3,5] A=1132 H=6
10	[0,3,10] A=1730 H=6	[8,3,10] A=1551 H=6	[16,3,10] A=1493 H=6

Variation mapping is useful for presenting parameter interactions but it sometimes feels trapped within the box of the parameter ranges set upfront. An also useful approach is to present maps of unique parameter combinations which seem visually the most interesting. Those capture species outside the realm of making small changes and viewing the results. Sometimes extreme parameter values produce quite interesting and unexpected results.

[40, -3, 10] A=2038 H=6	[90, 3, 1.5] A=1190 H=6	[50, 3, 30] A=4515 H=6	[0, 3, 67] A=3990 H=6
[0, -2, 128] A=2664 H=4	[0, 1, 320] A=1657 H=2	[0, 1, 512] A=1406 H=2	[512, -2, 1] A=2136 H=4
[216, 2, 5] A=2660 H=4	[434, 2, -14.5] A=1491 H=4	[512, -15, -20] A=13340 H=30	[764, 1, -1021] A=1607 H=2

Desirability Mapping

You will notice that for each design option we also computed a pair of metrics: the surface area and height. Those capture some partial quantitative information about each design option. We may use those as performance indicators by first relating them to semantic and contextual information; metrics by themselves mean nothing as they are just numbers.

As we aim to 3D print a surface we can associate its height with the time required for production. Additive manufacturing works by building an object layer by layer. The number of layer is related to an object’s height. Therefore, height is proportional to the time required to print all layers. The conclusion is that the smaller the height the faster the printing process.

Height = 0mm	2mm	4mm	6mm	30mm
[*, 0, *]	[0, 1, 320]	[512, -2, 1]	[90, 3, 1.5]	[512, -15, -20]

Surface area captures a sense of the geometric complexity. While 3D printing allows us to produce objects of any geometric complexity, it has a finite resolution related to the size of extrusion nozzle or layer height. This means surfaces with very fine details will suffer from lack of fidelity. The conclusion is again here that the smaller the surface area the better the print quality.

961	1132	2038	2515	13340
[*, 0, *]	[16, 3, 5]	[40, -3, 10]	[50, 3, 30]	[512, -15, -20]

The combination of those two metrics, for example using their product, tells us that the best results, in the sense of minimization, will be achieved by just printing a flat surface. This is to warn that just following numbers blindly can lead to meaningless results devoid of design sense.

What may do instead is to use a map where we categorize design options both qualitatively and quantitatively. For qualitative evaluation we use categorical labels instead of numeric values. They capture preference order from lowest to highest in a relative sense instead of absolute. In the table below we sort designs based on this notion of desirability from left to right with the first set containing options from the variation mapping study and the second from the experimentation study.

Less Desirable	→	→	→	More Desirable
[*, 0, *] A=961 H=4	[0, 3, 5] A=1221 H=6	[0, 3, 10] A=1730 H=6	[8, 3, 5] A=1154 H=6	[16, 3, 10] A=1493 H=6
[*, 0, *] A=961 H=4	[512, -2, 1] A=2136 H=4	[434, 2, -14.5] A=1491 H=4	[0, -2, 128] A=2664 H=4	[216, 2, 5] A=2660 H=4

Expressing a composite desirability design metric that captures both qualitative and quantitative aspects, is a very interesting topic but beyond the scope of this session. The process of selecting and sorting has already limited the range of options to a subset that both intuitively and numerically seem interesting as well as feasible. For experiments without prior experience at this point we need to choose and learn from the results.