Catmull-Rom interpolation on SVG Paths

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太阳男子

I am experimenting with creating high-performance, good-looking pencil tools using SVG paths.

I am logging the mouse coordinates to draw a path. To get a high-fideli

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2020-11-27 06:51
To answer your questions directly:
1. Yes. Catmull-Rom spline is an algorithm to interpolate a series of (x, y, z) points. It will generate a cubic polynomial curve between each two consecutive points.
2. You cannot direcly use Catmull Rom spline for SVG path. You need to convert it to cubic Bezier curve first.
For a curve segment defined by point P0, P1, P2 and P3 and knot sequence t0, t1, t2, t3, the centripetal Catmull-Rom spline (defined between point P1 and P2) can be computed by the recursive formula provided in https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline. Therefore, I will not elaborate here.

To convert it to cubic Bezier curve, you need to compute the first derivative at P1 and P2 as
```
M1 = (t2-t1)*(c1*(P1-P0)/(t1-t0) + c2*(P2-P1)/(t2-t1))
M2 = (t2-t1)*(d1*(P2-P1)/(t2-t1) + d2*(P3-P2)/(t3-t2))
```
Where
```
 c1 = (t2-t1)/(t2-t0),
 c2 = (t1-t0)/(t2-t0),
 d1 = (t3-t2)/(t3-t1),
 d2 = (t2-t1)/(t3-t1)
```
Then you can convert it to cubic Bezier curve with 4 control points: Q0, Q1, Q2 and Q3:
```
Q0 = P1
Q1 = P1 + M1/3
Q2 = P2 - M2/3
Q3 = P2
```
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耶瑟儿～

2020-11-27 07:06

I use interpolation cubics for this

sample point on
- mouse direction change in any axis
- if mouse traveled some distance for more precision can add: if the angle of direction change too much (I do not use this)
- if mouse stops (this can be ignored if you use on mouse up/down too)
use the sampled points as control points for interpolation cubic

see Interpolation cubic vs. Bezier cubic you find there also the transformation between interpolation and Bezier cubic

if that is not enough you can join lines with the same direction

Here an example of hand drawings in this way:

follow mouse

And the SVG:

<svg width="512" height="512" viewBox="-131.734968 -63.890725 383.802249 203.65153" >
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</svg>

It is around 20KB if you play with tresholds you can lower the point count significantly. This is tweaked to suit my needs.

Here example of how the mouse follow feels during drawing (captured in realtime during drawing)

spektre hand drawed

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