Question

I have an array of point data, the values of points are represented as x co-ordinate and y co-ordinate.

These points could be in the range of 500 upto 2000 points or more.

The data represents a motion path which could range from the simple to very complex and can also have cusps in it.

Can I represent this data as one spline or a collection of splines or some other format with very tight compression.

I have tried representing them as a collection of beziers but at best I am getting a saving of 40 %.
For instance if I have an array of 500 points , that gives me 500 x and 500 y values so I have 1000 data pieces.
I around 100 quadratic beziers from this. each bezier is represented as controlx, controly, anchorx, anchory.
which gives me 100 x 4 = 400 pcs of data.
So input = 1000pcs , output = 400pcs.

I would like to further tighen this, any suggestions?

Answer 1

By its nature, spline is an approximation. You can reduce the number of splines you use to reach a higher compression ratio.

You can also achieve lossless compression by using some kind of encoding scheme. I am just making this up as I am typing, using the range example in previous answer (1000 for x and 400 for y),

1. Each point only needs 19 bits (10 for x, 9 for y). You can use 3 bytes to represent a coordinate.
2. Use 2 byte to represent displacement up to +/- 63.
3. Use 1 byte to represent short displacement up to +/- 7 for x, +/- 3 for y.

To decode the sequence properly, you would need some prefix to identify the type of encoding. Let’s say we use 110 for full point, 10 for displacement and 0 for short displacement.

The bit layout will look like this,

Coordinates:        110xxxxxxxxxxxyyyyyyyyyy
Dislacement:        10xxxxxxxyyyyyyy
Short Displacement: 0xxxxyyy

Unless your sequence is totally random, you can easily achieve high compression ratio with this scheme.

Let’s see how it works using a short example.

3 points: A(500, 400), B(550, 380), C(545, 381)

Let’s say you were using 2 byte for each coordinate. It will take 16 bytes to encode this without compression.

To encode the sequence using the compression scheme,

A is first point so full coordinate will be used. 3 bytes.
B’s displacement from A is (50, -20) and can be encoded as displacement. 2 bytes.
C’s displacement from B is (-5, 1) and it fits the range of short displacement 1 byte.

So you save 10 bytes out of 16 bytes. Real compression ratio is totally depending on the data pattern. It works best on points forming a moving path. If the points are random, only 25% saving can be achieved.