Does that mean topology is more concerned with the pattern/shape, and geometry is more about measurement?
keeratsingh2002
I'd say so, yeah. Topology is more about the pattern or connectivity of the points (like vertices in a mesh), edges, and faces in a space. Geometry concerns itself with the specific measurements and properties of the space, such as lengths, angles, and areas, which give rise to the exact shape or form we see.
RishSharma7
I like to think of topology and geometry as two sides of the same coin - two different types of mathematics that allow computer graphics to be so advanced today. Geometry I find to be more rigid and locally focused, involving angles and oftentimes 2D surfaces (although that may not be the official way to describe it). Topology focuses on things like bending and turning, which in turn involves functions, differentiation, smoothness, etc. Regardless, I'm interested to see if this is something we should understand to a high degree (and if we'll be tested on it), because I might need a brush up on it myself.
ArjunPalkhade
I agree with Keerat, I feel that the specificity of edge-ordering and manner through which vertices can reach one another is more relevant to topology while geometry is overall shape/form. My assumption may be inaccurate, but I feel when manipulating objects with multiple parts, topology can drastically alter how it shrinks/grows and thus matters for modeling organic structures.
anavmehta12
So I found an intuitive example to understand the difference between geometry and topology is that a ping pong ball and egg have different geometry but the same topology as there surfaces are both continuous. However their geometries are different as an egg is an oval and a ping pong ball is a sphere.
mahumkhan1
I liked Anav's example of different geometry and the same topology. To complement that comment, I wanted to think of two objects with the same geometry but with different mesh topology. I was thinking maybe a cylinder and mobius strip fit that description as they both have the geometric shape of a rectangular band but the difference is that the mobius strip has only one side and one edge. I am not sure if this is a valid example because in this slide the same geometry seem identical with the exception of one vertex.
jacky-p
I agree with the previous comments, to my understanding topology deals more with the manipulation of shapes while geometry is more local and deals with the rigid aspects of shapes (exact points/lines). Topology are the preserved properties of shapes while they are undergoing changes like bending and stretching. Geometry is more to do with lines, angles, and curves of a specific shape. anavmehta12's example of the egg and pingpong is very helpful. Both objects have the same topology and different geometries (shapes), ones stretched out (oval) while the other is not (circle).
llejj
This seems similar to the idea that a topologist views a donut and coffee mug as the same, since they both have the same structure (one hole)
Does that mean topology is more concerned with the pattern/shape, and geometry is more about measurement?
I'd say so, yeah. Topology is more about the pattern or connectivity of the points (like vertices in a mesh), edges, and faces in a space. Geometry concerns itself with the specific measurements and properties of the space, such as lengths, angles, and areas, which give rise to the exact shape or form we see.
I like to think of topology and geometry as two sides of the same coin - two different types of mathematics that allow computer graphics to be so advanced today. Geometry I find to be more rigid and locally focused, involving angles and oftentimes 2D surfaces (although that may not be the official way to describe it). Topology focuses on things like bending and turning, which in turn involves functions, differentiation, smoothness, etc. Regardless, I'm interested to see if this is something we should understand to a high degree (and if we'll be tested on it), because I might need a brush up on it myself.
I agree with Keerat, I feel that the specificity of edge-ordering and manner through which vertices can reach one another is more relevant to topology while geometry is overall shape/form. My assumption may be inaccurate, but I feel when manipulating objects with multiple parts, topology can drastically alter how it shrinks/grows and thus matters for modeling organic structures.
So I found an intuitive example to understand the difference between geometry and topology is that a ping pong ball and egg have different geometry but the same topology as there surfaces are both continuous. However their geometries are different as an egg is an oval and a ping pong ball is a sphere.
I liked Anav's example of different geometry and the same topology. To complement that comment, I wanted to think of two objects with the same geometry but with different mesh topology. I was thinking maybe a cylinder and mobius strip fit that description as they both have the geometric shape of a rectangular band but the difference is that the mobius strip has only one side and one edge. I am not sure if this is a valid example because in this slide the same geometry seem identical with the exception of one vertex.
I agree with the previous comments, to my understanding topology deals more with the manipulation of shapes while geometry is more local and deals with the rigid aspects of shapes (exact points/lines). Topology are the preserved properties of shapes while they are undergoing changes like bending and stretching. Geometry is more to do with lines, angles, and curves of a specific shape. anavmehta12's example of the egg and pingpong is very helpful. Both objects have the same topology and different geometries (shapes), ones stretched out (oval) while the other is not (circle).
This seems similar to the idea that a topologist views a donut and coffee mug as the same, since they both have the same structure (one hole)