## reb Class REB_TrapShapeCassiniOvals

```Object
common:Generic
common:TrapShape
reb:REB_TrapShapeCassiniOvals
```

`class TrapShape:REB_TrapShapeCassiniOvals`

This shape uses the Cassini ovals function.

This variant of the function involves taking a square root so there are two solutions. A signed and absolute value version of the distance is also available. The transformed value is the complex return value of the function.

Ultra Fractal Source
``` class REB_TrapShapeCassiniOvals(common.ulb:TrapShape) {
; This shape uses the Cassini ovals function.<br>
; <p>
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"

; Constructor
func REB_TrapShapeCassiniOvals(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc

; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d =  0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
if @negroot
rr = 0.5*@a*(cos(2*theta)-((@b*0.1/(@a*0.5))^4-sin(2*theta)^2)^0.5)^0.5
else
rr = 0.5*@a*(cos(2*theta)+((@b*0.1/(@a*0.5))^4-sin(2*theta)^2)^0.5)^0.5
endif
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
return d
endfunc

default:
title = "Cassini Ovals"
int param v_trapshapecassiniovals
caption = "Version (Trap Shape Cassini Ovals)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecassiniovals < 101
endparam

float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam

float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
default = false
endparam
}
```

Constructor Summary
`REB_TrapShapeCassiniOvals()`

`REB_TrapShapeCassiniOvals(Generic pparent)`
Constructor

Method Summary
` float` `Iterate(complex pz)`
Call this for each iteration being trapped.

Methods inherited from class common:TrapShape
`GetColorChannel, GetTextureValue, GetTransformedPoint, Init, IterateSilent, SetThreshold`

Methods inherited from class common:Generic
`GetParent`

Methods inherited from class Object

Constructor Detail

### REB_TrapShapeCassiniOvals

`public REB_TrapShapeCassiniOvals(Generic pparent)`
Constructor

### REB_TrapShapeCassiniOvals

`public REB_TrapShapeCassiniOvals()`
Method Detail

### Iterate

`public float Iterate(complex pz)`
Call this for each iteration being trapped.

Overrides:
`Iterate` in class `TrapShape`