DIGITAL MODELING AND PROTOTYPYING
Tuesday, September 3, 2013
MY PORTFOLIO-PADMAKUMAR
Thursday, August 1, 2013
AUTODESK FORCE EFFECT- A simple exercise
Monday, April 8, 2013
Product Design -Woofer
Wednesday, March 20, 2013
Woofer -ID
My sketchbook renderings
Monday, March 4, 2013
Now or Never
Exponentially increasing demand of human population has brought a situation of sucking the natural resources to the fullest. Over and above, the third world countries like India has a major role
in the contribution of "Environmental Pollution".
I live in a city called Bangalore in India, highly
populated city.
Vehicles burn gallons of petrol in the hectic traffic here. I don't know the level of particulates in the air and I don't believe(I don't trust ) the numbers provided.
I used to see exhausts emitting black smoke.
How a product interact with its environment during its life and after life? The products we design will have an impact on the environment where it works.
I would like to share a Book titled EARTH, INC. by Gregory Unruh, he talks about using nature's
rule to build sustainable profits.
Follow natures rule, stop dumping toxic materials that are not environmental friendly.
He talks about making sustainable profits by following the rules of biosphere.
I think as a designer, this book is worth spending your time.
Wednesday, August 24, 2011
What is Gaussian curvature?
What is Gaussian curvature?
The definition of Gaussian curvature in Wikipedia is as follows
In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ1 and κ2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is isometrically embedded in space. This result is the content of Gauss's Theorema egregium.
Symbolically, the Gaussian curvature Κ is defined as
K= k1 x k2.
where κ1 and κ2 are the principal curvatures.
I will explain the above definition with a simple example. We will consider a cylindrical surface and try to find the Gaussian curvature of that surface.
By the definition K=k1 x k2
We need k1 and k2 of each point where k1 and k2 are the min and max values respectively.
We create a point on the surface first, then a normal to the surface passing through the point and a tangent plane to the surface passing through the point.
See the image below.
We need to have few planes (say 8 here) to create Normal section curves. Means, we are going to create intersection curves using planes which pass through the surface normal and Normal to the Tangent plane. Our point on the surface is common to all Normal section curves. All the Normal section curves contain our point on surface.
See the figure below. First figure shows the planes for creating intersection curves and the second one shows the Normal section curves created using the Planes.
DTM1, DTM2, DTM3, DTM4 etc are the planes.
Next figure you can see the Normal Section curves.
Make a note that the curve highlighted in red is a straight line whose curvature is zero, means the k2 is zero (in this case).
Next I would like to see the maximum curvature (k1) at the point. I have curvature plot tool and right of the bat I will highlight the curvature combs of the above curves.
Now I have the curvature variation of all the 6 curves, see below
How will I find the maximum curvature at the point on surface? I know the parameter value for our point is 0.5 (point is at the mid of the curves you can see)
Curve Parameter | Curvature |
0.5 | 0.006666667 |
0.5 | 0.002988536 |
0.5 | 0.002526927 |
0.5 | 0.00063661 |
|
|
I found that the maximum curvature is 0.0067. The value of k1, if we consider only the above six curves will be 0.0067(Correspond to the circle)
But when the software calculates the maximum curvature, it looks for all the possible curves that can pass through our point on the surface.
Now what is K?
K= k1 x k2
= 0.0067 x 0
= 0
You take any point on the cylindrical surface the value of k2 will be zero corresponding to the straight line.
So K=0 over the entire cylindrical surface.
Now see the Gaussian Curvature display with color contour
The green color has a value of 0, you can see from the color spectrum.
A positive Gaussian curvature value means the surface is locally either a peak or a valley. A negative value means the surface locally has a saddle points. And a zero value means the surface is flat in at least one direction.
For a flat surface the Gaussian curvature will be zero. How? Self explanatory.
Thanks
PADMAKUMAR NAIR