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# 3d scan to calculate volume & weight

what we love about our 3d scanning-centric business is the diversity of our customers and of course their needs.

we’ve recently worked with a customer who wanted to get the weight of his objects at 40% magnification. the customer has a physical object at its original scale. for simplicity, let’s refer to the following:
--> original scale = object 1x
--> 40% magnification = object 1.4x

as we thought about how to arrive at what the customer needs, we thought okay, the solution can be derived from common formulae that we studied in our early schooling years. 3d scanning would produce object 1x’s volume. scale up the 3d mesh by 40% and we’ll get the object’s 1.4x volume. multiply 1.4x volume with material density and voila, we get the weight of object 1.4x!

case closed. but then, a job wouldn’t be done well if no cross checks are done, right? so we bravely checked for variation of object 1x’s weight vs object 1.4x’s. that number isn’t 1.4, in fact it’s a much larger number. so a period of vigorous head-scratching & investigation ensued.

our findings are very very interesting (albeit rather geeky):
1) remember your mom told you to pay attention in school? well, that’s important, but so are memory & probing
2) you cannot simply multiply the magnification factor (maFA) to volume or weight to get the corresponding volume or weight. for example, volume 2x is NOT volume 1x * 2. the same applies for shrinkage.
3) for any given maFA, the resulting magnification multiplier (maMU) is the same even if the shape/geometry are different so long as the volume is constant. cylinder, cube, sphere, bird-shaped container, etc. will share the same maMU given a constant maFA & volume.
4) all maMU of any maFA can be easily calculated in the same manner.

let’s try a cylinder.

then, let’s try a sphere.

let’s now look at the 3 tables above. notice the patterns highlighted in corresponding colours. this was our big aha moment.

maMU in the last column stands for magnification multiplier. maMU is the correct multiplier to use to get the projected volume of object 2x, when we know volume of object 1x. it is wrong to use 2 as the maMU. do not confuse maFA with maMU.

still not convinced by the numbers? let’s look at this kerfuffle visually.

any 3 dimensional object is defined by its position in 3 coordinates, the x, y, & z.

when we double the volume of object 1x, essentially creating object 2x, it is wrong to simply multiply object 1x’s volume by 2.

when the volume of object 1x is doubled, its dimensions in those 3 coordinates (x, y, z) are doubled.

okay, now that we’ve covered regular shapes, what about irregular shapes? do the same workflow & formula apply?

to answer that question, let’s first go back to the cube example. imagine that the cube is a container filled to the brim with gold powder. the volume of the gold powder automatically becomes 1,000mm3. so far so good.

now, think of another container in the shape of a can that has been kicked about and whose shape has subsequently become irregular due to the many dents that define its new geometry. so let’s pick this can up and fill it to the brim with gold powder. the volume of gold powder will remain 1,000mm3 so long as the dented can’s volume is 1,000mm3. the shape really doesn’t matter as long as the volume remains constant. note that the can in its original uniform shape has a volume of more than 1,000mm3.

think about it another way:- a 1,000mm3 volume can take an infinite number of forms - regular, irregular, boxy, elongated, spherical, worm-like, spiky, and so on. what will differ across these shapes are their dimensions (width, length, height, radius, etc.).

so, how do we derive weight out of volume then?
weight (or mass) = volume * density.
note that weight is considered equal to mass on planet earth due to a constant gravitational field strength.

since we know the volume of the magnified object, and we know which material we want the object to be manufactured in, what we need is the magic number (the density of that desired material). the rest is easy multiplication.

relationship between mass & volume is simple, it’s a straight line. why straight line? because this very line represents the density of a specific material, which would remain constant under constant environmental factors (temperature, pressure, etc.).

what this really means is that we can use the very same magnification multiplier (maMU) that we used for volume for mass. if we know the mass of object 1x to be 10g. we can be sure that the mass of object 2x is 10 * (1 + 700%) = 80g. likewise for object 1.4x which is 27.44g (10 * (1 + 174.40%)).

the best part is that we are not limited to the maFA of 1.4x & 2x that we have covered above. the same workflow & formula apply to any & every maFA (1.03x, 50.1x, etc.). yay!

rapid precise calculation can be made not just for volume and weight. surface area and radius of curvature too can be quickly & accurately measured. 3d scanning is indeed very useful for calculating dimensions of complex, irregular geometries.

kitCAD3d’s artec leo 3d scanner is up to 0.1mm accurate and its superior tracking ability eliminates the need for target stickers. artec leo’s agility allows it to weave through narrow areas efficiently as it is cable-free, handheld, and isn’t tethered to the computer. it is no wonder that artec leo is used & trusted by many in heavy industries as well as entertainment.

artec 3d scanner brand originates from the EU & likewise its scanners are made in the EU.