# RegionPlot3D doesn't evaluate a set of conditions [closed]

A huge set of conditions

    cond={1440 (eta + 2 xsi) (9.81 + 0.003969 (1 + zeta)) >=
114.307 (1 + zeta),
114.307 (1 + zeta) >=
1440 (eta - 2 xsi) (9.81 + 0.003969 (1 + zeta)),
1440 (9.81 (2 + eta - 2 xsi) +
0.0068431 (-11.6 + 0.58 (eta - 2 xsi)) (1 + zeta)) >= 0,
1440 (9.81 (-2 + eta + 2 xsi) +
0.0068431 (-11.6 + 0.58 (eta + 2 xsi)) (1 + zeta)) <=
0, -783.333 <= -0.275369 (78.2399 eta + 1560.9 (-1 + xsi) -
3.90224 (1 + xsi)), -0.275369 (78.2399 eta + 1560.9 (-1 + xsi) -
3.90224 (1 + xsi)) <= 783.333, -783.333 <=
0.249143 (78.2399 eta + 1560.9 (-1 + xsi) - 3.90224 (1 + xsi)),
0.249143 (78.2399 eta + 1560.9 (-1 + xsi) - 3.90224 (1 + xsi)) <=
783.333, 2482.76 (0.000443649 (78.2399 eta + 1560.9 (-1 + xsi) -
3.90224 (1 + xsi)) + 0.0184162 (1 + zeta) -
0.232 (eta + 2 xsi) (9.81 + 0.003969 (1 + zeta))) <= 0,
2482.76 (-0.000443649 (78.2399 eta + 1560.9 (-1 + xsi) -
3.90224 (1 + xsi)) + 0.0184162 (1 + zeta) -
0.232 (eta + 2 xsi) (9.81 + 0.003969 (1 + zeta))) <= 0,
2482.76 (-0.000401397 (78.2399 eta + 1560.9 (-1 + xsi) -
3.90224 (1 + xsi)) +
0.4 (-0.0460404 (1 + zeta) +
0.58 (eta - 2 xsi) (9.81 + 0.003969 (1 + zeta)))) <= 0,
2482.76 (0.000401397 (78.2399 eta + 1560.9 (-1 + xsi) -
3.90224 (1 + xsi)) +
0.4 (-0.0460404 (1 + zeta) +
0.58 (eta - 2 xsi) (9.81 + 0.003969 (1 + zeta)))) <= 0}


define a region in 3D

I would like to create a RegionPlot3D

RegionPlot3D[ AllTrue[cond], {xsi, 0, 1}, {eta, -1, 1}, {zeta, -1, 20} ]


but Mathematica doesn't evaluate.

What could be the reason ? Is there a workaround?

Thanks!

• RegionPlot3D[And @@ cond, {xsi, 0, 1}, {eta, -1, 1}, {zeta, -1, 20}] ?
– Syed
Jan 29 at 16:50
• @Syed Such a simple solution, thank you very much. Couldn't step away from my AllTrue attempt... Jan 29 at 16:59
• @Syed Followup problem: Is it possible to extract the "Volume" as an implicit region from a given RegionPlot3D  ? Thank You! Jan 30 at 11:05
• reg = ImplicitRegion[And @@ cond, {xsi, eta, zeta}]; and Volume@reg gives 3.11594 and the RegionMeasure[reg, 3] gives the same result, albeit with some delay. I don't have enough insight to say if it is correct, but you can provide feedback. Thanks.
– Syed
Jan 30 at 11:11
• @Syed Thanks for your fast response. Unfortuantely Region[reg] only shows a blanc cell. Jan 30 at 11:16

RegionPlot3D[And @@ cond, {xsi, 0, 1}, {eta, -1, 1}, {zeta, -1, 20}]


OR

RegionPlot3D[
AllTrue[cond, # == True &], {xsi, 0, 1}, {eta, -1, 1}, {zeta, -1,
20}]


• RegionPlot3D[ AllTrue[cond, Identity], {xsi, 0, 1}, {eta, -1, 1}, {zeta, -1, 20}] would also work and look less awkward.
– Syed
Jan 29 at 18:55