Mathematically accurate curved surfaces


The curved surfaces in SketchUp are not mathematically accurate, so volumetric calculations on curved surfaces aren’t exact.

I’d like to propose a curved surface toolset that makes mathematical curves and surfaces to increase the accuracy of SketchUp. I’m not sure what types of tools would be in the toolset or how SketchUp could make accurate non-polygonal spheres, but I’d like a minimal amount of tools (for ease of use) that can make almost any type of curved surface. A sphere only has one measurement, the radius, so SketchUp shouldn’t need to store the coordinates of all the vertices in a sphere if it only need a radius to define the sphere. The new SketchUp sphere could be a single two-sided surface instead of being made of many faces. I’m not sure if this would be possible, but for more complex geometry, maybe SketchUp could store mathematical equations to define the curved surfaces. To clarify, the user wouldn’t have to input mathematical equations, but SketchUp would store curved geometry with mathematical equations in it’s memory. Equations are usually shorter than a list of coordinates for thousands of points.


SketchUp only models in poly so you cannot make true Curves. Doing so would require much more than a new tool but an entire reworking of the engine.

If you want to get serious about curves I would suggest Rhino as it’s interchangeable with the native .skp format.

Ed: You can use Blender for free but it’s not interchangeable with SketchUp.


If that’s true, then I think upgrading the program be worth the added accuracy with curves. A common complaint about SketchUp is it’s inaccuracy with curves, so an upgrade with a “curved surface” toolset could improve SketchUp. Maybe SketchUp Pro 2019 or 2020?


But that would be transforming SketchUp into a new thing, the whole point of SketchUp is thats it’s simple and un-bloated like most other software. There are so many curve editors (that are amazing!) but they are only really good at that, they don’t offer what SketchUp does. If you start mixing it up then it’s likely that SketchUp will loose all of the things it’s good at. In most cases, I can achieve (for visualisation results) something in SketchUp in half a day that would take somebody a few days using a traditional curve editor. However anything I create could never be used for fabrication but if thats what you need, simply modeling in curves is only a small part of the checklist.

You only really need curves if you are working with fabrication, and if that’s the case you are almost 100% working with other software as you are in a professional environment. One of the issues for example is the amount of polygons a simple NURBS surface translates to. A simple curve surface of 5MB can translate to 100’s MB when converted to polygons.

They key is using SketchUp in a workflow with other software and plugins, using the strength of each tool.


When you hold an idea as sacred and refuse to change it, you’re limiting it’s potential. The inaccurate curved surfaces in SketchUp are a problem, so figuring out a solution would improve SketchUp. Mathematical curves don’t have sides, so curves shouldn’t have sides in the modeling program either.

One of my favorite things about SketchUp is it’s simplicity. If they do upgrade the accuracy of their curves, then I hope they would keep their simplicity too. One solution to keep the simplicity is to upgrade the pre-existing arc & circle tool, so they are accurate mathematical curves. There would be the same amount of tools as before and if someone wanted to make a faceted curve, then they could just type in the amount of sides. Although, the default curve would be mathematically accurate. If you want to convert the curves into polygons, then you could use “explode curve” in the right click menu. The less changes the better, but the more accuracy the better too. SketchUp is meant for professional work, so having accurate curves is a must if SketchUp wants fabrication companies as customers. There are even instances where having inexact curved surfaces could be a problem for architects. For example, what if they want to measure the volume of a curved window, curved wall, or something?


The main problem is that curve modelling is not just an ‘extra’ toolset you can turn on. If you are going to use that method you need a fully comprehensive amount of tools and options. Thats why if you look at the Rhino interface it looks the way it does, and Blender to some respect.

The main questions is why would you want that type of accuracy in SketchUp and not use an existing tool that already performs this function exceptionally well?

What is it that you or others are trying to make in SketchUp, and for what purpose, that you need to be able to export curves?

I work with curves in work (not myself but I often have to covert curves to poly). We only have the curves in CAD because those elements have to be fabricated or go into real simulations. For visualisation work, rendering, illustration, animation. Curve based models are all unsuitable and you can spend days preparing them so you can just make a simple 2D render.

I can see why you may want it if you only prefer to use SketchUp, but my advice would be to just use a companion app that does it already very well.


SketchUp’s pre-existing curve tools do work exceptionally well, but the curved surfaces do not calculate an accurate volume. They give a rough calculation. If you’re working with curved surfaces, then the pre-exisitng tools might give inaccurate measurements. What if an architect wanted to design a monolithic dome and calculate the amount of concrete needed for it? A rough calculation of its volume might cost the architect wasted time and money. They might not get enough materials, then have to make a second order and accidentally get excess concrete. If SketchUp upgraded the mathematically accuracy of it’s curves, then it could allow architects to use more curves in architecture more freely.


What if an architect wanted to design a monolithic dome and calculate the amount of concrete needed for it?

Normally they would use other tool sets for these precise calculations.


Wouldn’t it be easier if they just could do those calculations in SketchUp (assuming the upgrade doesn’t bloat the menus with tons of extra buttons and add obscure command names)? Also, if the dome isn’t completely mathematically precise, then that could affect the measurements of other components in the design such as wall stud heights and stuff.


I also wish that SketchUp worked with true arcs and circles. To me it is not a “feature” that SketchUp approximates arcs with straight segments, it is a deficciency. I presume the reason SketchUp uses straight-segment approximations is so that intersection calculations, follow-me, push-pull, scale, move, etc. are significantly easier for the software to calculate - not because the developers thought that approximations are better.

Speaking as a professional software engineer for the past 37 years (including a moderate amount of geometric and graphics programming), I will grant that the mathematical calculations to manage true curves and curved surfaces across the range of entity manipulations that a SketchUp user can easily perform would be very complex. Nevertheless, I wish that SketchUp were written to support them. I don’t see why the user interface would necessarily become more complicated to support true circular arcs (which could subsequently be distorted). Adding true arcs does not require supporting other shapes such as bezier curves, parabolas, etc.

FYI, I use SketchUp Pro as a hobby user, working on a rather serious project (documenting an historic spacecraft from the 1970s) but which I do for pleasure, not business. Even so, one of my real worries in choosing to use SketchUp five years ago is that the curve approximations would haunt me. They can be quite zig-zaggy when intersecting each other, but I’m living with it. Time will tell.


It’d be cool if the upgrade allowed you to convert polygonal curved surfaces into real curved surfaces, so you wouldn’t have to redraw the entire spacecraft to manually convert it into mathematical curves. And vice-versa (real curves to polygons). Although, I’m not sure if that’d be possible considering the amounts of shapes SketchUp would have to analyze. Maybe if SketchUp got some AI, then it would be possible. I don’t know. Or it could convert softened geometry to curves, but keep normal edges creased.

I agree that SketchUp curves have deficiencies in accuracy, but I’d like to see the segmented arc tools stay, so people can draw things like this light…

You can use the polygon tool to make segmented circles, but maybe a segmented arc tool could be added in addition to changing the arc and circle tools to mathematical curves. The tools are labeled the arc tool and the circle tool, so it’d make sense to have them make mathematical arcs and circles like their names suggest.


As great as SketchUp is, it’s better to know what it CANT do well. I’d just calculate the volume of sphere the old fashioned way…that way there’s less risk of error and we can continue using SketchUp for it’s strengths without worry.


For people who aren’t very good at math, like myself, calculating the volume of a monolithic dome could be a very time-consuming task or even an impossible task. Especially if the dome is an irregular ellipsoid of some type with various organic cutouts.

For something as simple as a sphere, that’s totally doable though. Although, I admit, it took me a good 20 minutes to do my calculations in the initial post. I’m just so used to the computer doing the math for me, so I haven’t had the need. The part that was most difficult for me was converting the cubic inches to cubic feet. After relearning it, I get it now & could calculate a sphere’s volume quickly, but accurate volume calculations in SketchUp could’ve helped speed up the initial volume calculation process… and it would still speed up complex volume calculations (like the monolithic dome’s volume).

On a side note: I’ve just developed an interest in math because math can increase the organization in my designs. Mathematical surfaces are so beautiful, so I think they’d be great design elements.


You might take a look a U-V Polygen. While still using planar facets, you can increase the number to give good approximations … especially in the area of 3D printing.


Alas, though this feature would sometimes be very valuable, I think that the core engine of SketchUp was designed and built around the math of lines and planes. If I’m right, extension to true curves though not impossible would require a very massive rewrite (with all the potential for bugs such a thing always brings) and could possibly have a serious impact on performance.


Certainly, but I don’t think it would be beyond the capabilities of the SU Team.

At least Rhino is not very slow and it runs on quite simple hardware.Probably working with large models might even improve, as NURBS modellers can optimize in many ways the number of polygons they create for display.
NURBS geometry would dispense with the current too short edges limitation and the errors generated due to that in the boolean tools, for instance.


A question of priority and business goals, not of capabilities :wink:


Indeed, I do not expect SketchUp to ever model true arcs - low business priority, high development costs. I wish it would (which is why I expressed support in this thread) but I presume it won’t.


I’m reminded of my basic calculus courses and my first computer program to calculate the area under a curve. The bottom line is, imho, that working with digital models will always result in digital answers – i.e., not perfect analog answers. If you want more precision, make your curves out of more segments. And I’m pretty sure they don’t load concrete trucks to the nearest cubic inch.


That’s true. The high poly models are close to the actual volume. It’s still a little inaccurate when the model has curved surfaces, but it’s definitely possible to design a monolithic dome or something curvy in SketchUp.

Edit: This is most accurate volume I could get on a house-sized hemispherical dome. I tried to make a higher poly one, but I decided to force quit after watching the spinning beach ball of doom for a few minutes. Had I waited, it probably would have given a more accurate measurement (possibly only a few cubic inches off). Either way, 2.98 cubic feet off isn’t that bad for a house that size. You’re right. It probably wouldn’t be a problem. Worst case scenario, someone uses a low poly curved surface to figure out the volume causing their estimate to be way off.