Information about California's commission process is here and here.
There is no easy technological fix because there are multiple legitimate considerations and no objective method of weighting them.
For example, look at the map of South America as if it were a legislative districting. That border between Chile and Argentina is an obvious gerrymander, right? Well, no. It reflects the reality that today, and even more so when the line was drawn, the Andes Mountains presented a significant barrier to travel. It makes sense that someone on the Chilean side should be in the same district as someone 300 miles to the north rather than someone 50 miles to the east.
As that example shows, calling for a "simple geometrical shape" doesn't always make sense. In particular, there are a couple of factors that have a good claim to being objectively reasonable and yet tend to help Republicans. One is that district lines should, where feasible, respect existing political boundaries. "The First District consists of Skinnertown, Eladville, Earl G City, and part of Kosberg." If the municipal boundaries, dating back many years, are somewhat contorted, that district may be less than perfectly compact. Nevertheless, it makes it easier for people to know which district they're in, and it groups together people who presumably have some common interests. The trouble is that Democrats are often concentrated in larger cities. Therefore, this criterion will often produce a few urban districts that are packed with Democratic voters, leaving Republican majorities in a larger number of rural and suburban districts.
Another important factor is representation of ethnic minorities (in the U.S., blacks and Hispanics). History demonstrates that it's hard -- not impossible, but hard -- for people from these communities to be elected in districts in which they're the minority. The solution is the creation of "majority minority" districts. Linking together pockets of minority voters requires some districts that look preposterous, like NC-12 for blacks and IL-4 for Hispanics. Such districts also tend to concentrate large numbers of Democratic voters. (Those two examples have Cook Partisan Voting Index scores of D+26 and D+29, respectively.) That again enables Republicans to have the majority in more districts.
If you tried to redistrict based solely on a mathematical algorithm, you could split up some cities and abolish majority-minority districts.
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