Circos > Documentation > Tutorials > Recipes > Link Geometry
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# 8 — Recipes

## 2. Link Geometry - Detailed Bezier Control

The raison d'etre of Circos is the ability to draw links. Links are covered in tutorial 5. Link geometry is controlled by many parameters (see tutorial 5.2).

Below, I'll walk through some geometry recipes to help illustrate how the parameters interact.

### straight lines

To draw links with straight lines, keep bezier_radius undefined. Below I set the link radius to be nearly at the inner ideogram radius (0.98r). I also hide links associated with smaller segmental duplications (<1.5kb), set the thickness based on the size of the segmental duplication (scaled exponentially in the range 1-6), and color red those links that eminate from a region on chromosome 2.

```
# comment out bezier_radius, or leave out

color        = vdgrey
thickness    = 2
file         = data/5/segdup.txt

<rules>

<rule>
importance = 110
condition  = _SIZE1_ < 1.75kb || _SIZE2_ < 1.75kb
show       = no
</rule>
<rule>
importance = 100
condition  = 1
thickness  = eval(max(1,min(6,exp(_SIZE1_/50000))))
flow       = continue
</rule>
<rule>
importance = 90
condition  = (_CHR1_ eq "hs2" && abs(_START1_ - 100Mb) < 20Mb) || (_CHR2_ eq "hs2" && abs(_START2_ - 100Mb) < 20Mb)
color      = red
</rule>
</rules>

```

Notice that you can use common suffixes like kb and Mb to indicate a value multiplier.

### bezier curves

Straight lines are not always the best way to draw links, especially for links that join two closely spaced points. The bezier_radius parameter, when defined, controls the curvature of the line by establishing a third control point of the line at an angle that bisects the position of the start and end of the link.

The bezier_radius specifies the radius at this control point. Using the start and end of the link, and the control point, a bezier curve is drawn. Note that the bezier curve generally does not pass through the control point, but merely comes close.

Thus, the larger the bezier radius, the greater the affinity of the middle of the link line to the ideogram circle. A bezier_radius of zero, on the other hand, will result in great affinity of each link to the center of the circle.

You generally will be setting the bezier_radius as a relative value. It will be relative to the inner ideogram radius.

```bezier_radius = 0.25r
```

You can set the bezier_radius to be negative, which will result in some weird link layouts (the control point will be placed at the same radial position but on the other side of the circle).

### dynamically altering geometry parameters

You can use rules to adjust the bezier_radius. For example, links between closely spaced points on the same ideogram should get a large bezier radius to avoid the link from being drawn too far into the circle, only to double back on itself. In the rule below, any intrachromosomal links with ends within 50Mb will have a bezier_radius of 0.75r (vs all other links with bezier_radius of 0.5r, for example).

```<rules>
<rule>
importance    = 95
condition     = _CHR1_ eq _CHR2_ && abs(_START1_-_START2_) < 50Mb
flow          = continue
</rule>
</rules>
```

You can also dynamically remap the bezier_radius using an eval() condition. For example, the rule below will adjust it to range from 0.5r to 0.9r smoothly (links 100Mb apart will have a bezier_radius of 0.5r which will increase to 0.9r as the link ends fall closer). The unit "r" has to be explicitly concatenated onto the new bezier_radius in the eval() expression.

```<rule>
importance     = 95
condition      = _CHR1_ eq _CHR2_ && abs(_START1_-_START2_) < 100Mb
bezier_radius  = eval( (0.5 + 0.4*( 1 - abs(_START1_-_START2_) / 100Mb )) . "r" )
flow           = continue
</rule>
```

The choice of parameters in the rules (0.5, 0.4, and 100Mb) are arbitrary and guided by desired esthetics of the final image.

### making link ends perpendicular to ideograms

As you can see from the images in the previous examples, links with ends that are far apart impinge on the ideogram at a shallow angle.

If you would like the link lines to be perpendicular to the ideogram, additional curve control points are necessary. To do this, the crest parameter is used to set two additional control points at the same angular position as the link start and end, but at a radial position closer to the center of the circle (see tutorial 5.2).

The crest parameter is automatically relative to the link radius and bezier radius. When crest = 0 (no effect), the crest control point is at the same radial position as the link start/end. When crest = 1, the control point is placed at the bezier_radius (see this image from tutorial 5.2).

Rules make it easy to hide links that are do not fit a condition. For example, to draw only interchromosomal links (between different chromosomes), hide all intrachromosomal links

```<rule>
importance = 100
condition  = _CHR1_ eq _CHR2_
show       = no
</rule>
```

You can deal with interchromosomal and intrachromosomal links separately by either (a) setting up two tracks with two different hide rules (one track will have interchromosomal links hidden, the other intrachromosomal links hidden) or (b) setting up two sets of rules (one or more rules for interchromosomal links and one or more rules for intrachromosomal links).

```
<rules>

# intrachromosomal links with ends within 40 Mb placed outside circle

<rule>
importance = 90
condition  = _CHR1_ eq _CHR2_ && abs(_START1_-_START2_) < 40Mb
crest         = 1
color         = red
</rule>

# all other intrachromosomeal links hidden

<rule>
importance = 80
condition  = _CHR1_ eq _CHR2_
show       = no
</rule>

# of chromosome are inside circle

<rule>
importance = 70
condition  = _CHR1_ ne _CHR2_ && (_START1_ < 20Mb || _START2_ < 20Mb)
color      = black
crest         = 1
</rule>

# all remaining links are hidden

<rule>
importance = 10
condition  = 1
show       = no
</rule>

</rules>

```