# Tracking Curves

## Contents

## Introduction

http://uk.youtube.com/watch?v=wJ7C-FcxAy0 shows an example of a layer following a moving curve, and rotating to follow the curve as it moves.

How was that achieved? It's currently quite complicated to set up an arrangement like this in Synfig Studio, so I'll describe here how it works.

Hopefully in time someone will come up with a better design can be used to make it a lot more intuitive. I'm imagining that the Synfig back-end and .sif file format will remain the same, but some extra functionality will be added to the Synfig Studio GUI to allow the user to quickly and easily say "make this layer follow this bline and rotate with it" or some such. Ideas welcome!

## Discussion

If you download the .sif file and load it into Synfig Studio, it really isn't easy to see how the effect is achieved. A large part of the problem is that in Studio, when you convert a ValueNode using one of the conversion types, Studio doesn't indicate which conversion type was used. There is room for improvement here.

## Details

### Overview

The animation lasts for 32 seconds and has 3 top-level layers. This is a very simple animation other than the two parts with links (below), which control the location of the moving blob and the shape of the white beam of light respectively. These two parts are described separately.

The three top-level layers are as follows:

- moving blob - An encapsulation of three layers. Its origin is connected to the exported ValueNode "moving point". The three layers are:
- direction of movement - The fuzzy white beam of light. This is a simple bline with a feather of 0.3 units to make it fuzzy. Its vertices are connected to the ValueNode called "beam of light".
- inner circle - The smaller yellow circle. Not animated at all.
- outer circle - The larger red circle. Not animated at all.

- line - The moving curve which the object follows. It has waypoints at 0s, 16s, and 32s to make the line move. I exported four of its animated ValueNodes so that I could use them later. The exported four ValueNodes are:
- vertex1 - The position of the beginning of the curve
- vertex2 - The position of the end of the curve
- tangent1 - The tangent at the beginning of the curve
- tangent2 - The tangent at the end of the curve

- black background - A solid black background. Not animated at all.

### Moving Point

The "moving point" ValueNode represents the point on the moving bline where the circles are currently centered. It is an exported ValueNode of type "Segment Vertex". It has 2 components which determine the vertex that is used as its value:

- segment - The curve to follow, defined by vertex1, vertex2, tangent1, and tangent2, as exported from the 'line' layer above
- amount - A number ranging from 0 to 1, which indicates how far along the segment to go. 0 means "use vertex1" and 1 means "use vertex2". I want the point to travel along the curve sinusoidally, meaning it will travel fastest in the middle and slow to a momentary stop at either end. This makes the movement look smoother than using a linear movement. I called this ValueNode "((sin(angle))/2+0.5)", since that is how its value is calculated. The sin() function returns a number between -1 and 1, and I want a value between 0 and 1, so I halve the sin() value, giving -0.5 to 0.5, then add 0.5 to it, giving 0 to 1. Consequently, this 'amount' value is the result of a subtraction, LHS-RHS:
- LHS - The left hand side of the subtraction. I called this ValueNode "((sin(angle))/2). This will range from -0.5 to 0.5, and is the result of the 'sine' convert type, sin(Angle)*Amplitude:
- Angle - This is connected to "linearly changing angle"
- Amplitude - This is used to scale the value. Since I want sin(Angle)/2, the value is a constant 0.5.

- RHS - The right hand side of the subtraction. I wanted to add 0.5 to sin(angle)/2, but synfig only offers subtraction, so I subtracted -0.5 instead, which is the same. Thus, RHS is a constant Real ValueNode, with value -0.5

- LHS - The left hand side of the subtraction. I called this ValueNode "((sin(angle))/2). This will range from -0.5 to 0.5, and is the result of the 'sine' convert type, sin(Angle)*Amplitude:

### Beam of Light

The "beam of light" ValueNode is a two-point bline, with vertices as follows:

- Vertex001 - This is the vertex at the centre of the circle. It doesn't need to move, since the circles don't move. What moves is the "moving blob" layer, the encapsulating layer which contains this line and the two circles. So this vertex has a constant position of (0,0)
- Vertex002 - This is the other end of the fuzzy white beam. It was a width of 5 units to make the beam diverge. Its position is connected to the ValueNode called "scaled tangent".

### Scaled Tangent

The "scaled tangent" ValueNode is the offset vector from the center of the circles to the wide end of the beam of light.

This ofset needs to be a vector in a direction parallel to the tangent to the moving curve at the current point. This was achieved using the Scale convert type, with 2 sub parameters:

- Link - This is the vector to scale
- Scalar - This is the amount to scale it by. BLine curves have tangents which point from the start vertex towards the end vertex, along the curve. I want my beam of light to point in the direction of travel, which is sometimes towards the start of the curve and sometimes towards the end. To do this I needed to multiply the "tangent" ValueNode above by a number which would be negative when travelling towards the start of the curve. It just so happens that sin(angle+90) has exactly that property, and also has the benefit of making the beam get longer as the movement speeds up. So I called this ValueNode "(sin(angle+90))" and defined it as a "Sine" convert type, defined as value=Amplitude*sin(Angle):
- Angle - This needs to be "Angle+90", so it's defined as a subtraction (Synfig has a 'subtract' convert type, but no add). value = LHS-RHS:
- LHS - The left hand side of the subtraction - this is connected to "linearly changing angle"
- RHS - The right hand side of the subtraction. It's a constant -90.

- Amplitude - This is a constant 0.4, which simply scales the length of the beam of light down to keep it mostly on the screen.

- Angle - This needs to be "Angle+90", so it's defined as a subtraction (Synfig has a 'subtract' convert type, but no add). value = LHS-RHS:

### Linearly Changing Angle

The "linearly changing angle" ValueNode is the constantly changing angle that drives the whole animation. Whenever the angle increases by 360 degrees, the output of sin(Angle) does one complete cycle from 0 -> 1 -> 0 -> -1 -> 0. The angle changes linearly, using the Linear convert type, which has 2 parameters:

- Rate - How many degrees per second to increase. In the animation this is set to a constant value of 45 degrees per second. This means that one complete cycle (from the center to the right end, to the left end, and back to the center) will take 360/45 = 8 seconds to complete. This gives us four complete cycles in the 32 second animation.
- Offset - The value at the beginning of the animation (time = 0). Changing this to 90 for example will make the blob start at the right-hand end of the line. while changing it to 180 will make the blob start in the middle, but facing (and traveling) left.