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===== Virtual Laser Scanner ======

==== Introduction ====

The ”Scanner” is a module implementing a virtual laser scanning device. To use it, first import the module :

> import de.grogra.rgg.Scanner ;

and create a new instance :

> Scanner ls = new Scanner() ;

Then, the process of points acquisition can be seen as follow :

  - set a ray ”length” ;
  - set an origin, and directions for the rays ;
  - shoot the rays, store the returned data ;
  - repeat until enough points are acquired. This process can be done step-by-step, or a method implementing a scanning according to some predefined schedule can be used.

==== Shooting of the rays ====

The rays are always shot according to two angular parameters ($\theta_{range}$ , $\phi_{range}$) defining the solid angle that will be scanned, two parameters ($\theta_{step}$ , $\phi_{step}$) defining the resolution with which it will be scanned, and a direct orthonormal basis ($\vec{x}, \vec{y}, \vec{z}$) serving as reference (see below).

In the spherical coordinate system i based on the reference basis ($\vec{x}, \vec{y}, \vec{z}$), rays are shot for 
$\theta \in \left[\frac{-\theta_{range}}{2}, \frac{-\theta_{range}}{2}\right]$ 
with an angular resolution $\theta_{step}$ and for 
$\phi \in \left[\frac{\pi}{2}-\frac{-\phi_{range}}{2}, \frac{\pi}{2}+\frac{-\phi_{range}}{2}\right]$ 
with an angular resolution $\phi_{step}$ 
(see illustration Fig.1 p.2). Thus, the mean direction of the rays shot is $\vec{x}$.

Details concerning the spherical and cylindrical coordinate system used in
this module can be found at the end of this document (resp. 4.1 p.6 and 4.2
p.6).

{{:tutorials:fig_scanner.png}}

Figure 1: Directions of rays shot for the parameters $\theta_{range} = \frac{\pi}{2}, \phi_{range} = \frac{\pi}{4}, \theta_{step} = \frac{\pi}{20}, \phi_{step} = \frac{\pi}{8}$.

==== Methods available ====

**Remark : if calling multiple scan methods (e.g. //scan//, //scanCylinder//,
//scanSphere// ; see below) in a row, be sure to save the returned data
after each call, as they will not be kept.**

**Notations :** //Seg(Point3d point, Vector3d vector, Double l)// designates the segment which has the point //point// at one end, the direction vector //direction//, and
of length //l//.
//Cir(Point3d center, Vector3d normal, Double r)// designates the circle of //center//
center, of radius //r// and contained in a plane orthogonal to the vector //normal//.

**setRayLength** Sets the range of the rays.

> **void setRayLength(double desiredLength) ;**

//desiredLenght// must be strictly positive.

**setBasis** Sets the 3-dimensional basis to be used as reference for shooting the rays.

> **void setBasis(Vector3d x, Vector3d y, Vector3d y) ;**

The 3 vectors must form a direct orthogonal basis.

**setRange** &emsp; Sets the angular opening in θ and φ.

> **void setRange(double thetaRange,double phiRange) ;**


If $thetaRange \ge 2 · \pi$ (resp. $phiRange \ge \pi$) , then $thetaRange = 2 · \pi$ (resp. $phiRange = \pi$) will be used instead. $thetaRange \le 0$ (resp. $phiRange \le 0$)
sets an angular opening in //theta// (resp. //phi// ) of 0 (Note : //thetaRange = 0// and
//phiRange = 0// corresponds at the shooting of only one ray, along the x-axis).

**setSteps** Sets the resolution in //theta// and //phi//.

> **void setSteps(double thetaStep,double phiStep) ;**


If $thetaStep \ge thetaRange$ (resp. $phiStep \ge phiRange$) , then _thetaStep = thetaRange_ (resp. //phiStep = phiRange//) will be used instead. $thetaStep \le 0$ (resp. $phiRange \le 0$) sets an angular opening in theta (resp. //phi// ) of 0.

**setpDrawRay** &emsp; Set the probability of drawing one ray.

> **void setpDrawRay(double p) ;**

Each ray will be drawn with a probability //p// (if $p \le 0$ no rays will be drawn,
if $p \ge 1$ all the rays will be drawn), thus $n · p$ will be drawn in average (with //n// the total number of rays shot).

**scan**Triggers the scanning with the specified options.

> **ArrayList<Point3d> scan(Point3d center) ;**


Rays will be shot from the point center, according to the angular parameters
specified. Scanned points are returned in an ArrayList.

**writeDataToFile** Writes the ArrayList //data// in a file named //fileName//. The data are written according to a ”x y z” format.

> **void writeDataToFile(ArrayList<Point3d> data, String fileName) ;**


**scanSegment**  Moves the origin of the rays along the segment //Seg(startingPoint, direction, (nbSteps − 1) · stepLength)//. Rays are shot at each step according to the specified parameters. Scanned points are returned in an ArrayList.

> **ArrayList<Point3d> scanSegment (Point3d startingPoint, Vector3d
direction, double stepLength, int nbSteps) ;**


The vector //direction// must not be null, //stepLenght// and //nbSteps// must be strictly positive.

**Please note that for all the following methods, the angular pa-
rameters used are those fixed by the methods //setRange// and //setSteps//.
However, the basis defining the directions of the rays are defined
within the methods.**

**scanCircle** Moves the origin of the rays along the circle _Cir(center, normal, r)_. Rays are shot for each angular step //angleStep// until a complete circle has
been covered. Directions of the rays shot are defined by the local cylindrical basis $(-u, -u_{\theta}, normal)$ formed at each step, with respect to the reference basis $(zeroAngleVector, normal \land zeroAngleVector, normal)$. Scanned points are
returned in an ArrayList.

> **ArrayList<Point3d> scanCircle(Point3d center, double r, Vector3d
normal,Vector3d zeroAngleVector, double angleStep) ;**
> **ArrayList<Point3d> scanCircle(Point3d center, double r, Vector3d
normal, double angleStep) ;**

The vector _zeroAngleVector_ specifies the angle reference for the circle. It
must be orthogonal to normal. If none is specified, an arbitrary vector is used.

**scanCylinder** Moves the origin of the rays on the surface of the cylinder
of axis the segment _Seg(startingPoint, axis, (nbSteps-1) · lengthAxisStep)_ and
of radius _r_. For each step _i_ along the cylinder’s axis, the origin of the rays
revolves around the cylinder with an angular step _angularStep_. Rays are shot
at each angular step until a complete circle has been covered. Directions of
the rays shot are defined by the local cylindrical basis $(-u, -u_{\theta}, axis)$ formed at
each angular step, with respect to the reference basis $(zeroAngleVector, axis \land zeroAngleVector, axis)$. Scanned points are returned in an ArrayList.

> **ArrayList<Point3d> scanCylinder ( Point3d startingPoint, Vector3d
axis, double radius, double angularStep, double lengthAxisStep,
int nbSteps) ;**
> **ArrayList<Point3d> scanCylinder ( Point3d startingPoint, Vector3d axis, double radius, double angularStep, double lengthAxisStep, int nbSteps, Vector3d zeroAngleVector) ;**


The vector //zeroAngleVector// specifies the angle reference for each circle. It
must be orthogonal to //axis//. If none is specified, an arbitrary vector is used.

**scanSphere** &emsp; Moves the origin of the rays on a sphere of center center and
radius r. With respect to the spherical coordinate system based on the basis
(x,y,z), the origin of the rays moves from φ = 0 to φ = π with a step //phiStep//,
and, for each angle φ, from θ = 0 to θ = 2π with a step //thetaStep//. Rays are
shot for each couple (θ, φ), their directions being defined by the local spherical
basis $(−u_{r}$, $−u_{\phi}$, $u_{\theta})$. Scanned points are returned in an ArrayList.

> **ArrayList<Point3d> scanSphere (Point3d center, double r, double phiStep, double thetaStep, Vector3d x, Vector3d y, Vector3d z) ;**


//(x, y, z)// must be a direct orthogonal basis, r and //phiStep// must be strictly
positive. If $thetaStep \le 0$, then θ = 0 will be used at each step (thus the origin
of the rays describes an half circle).

**Noise simulation** &emsp; A set of methods enables noise simulation. The introduction of a noise factor is triggered for the parameters θ, φ and the hit distance by the following methods: 

> **void setThetaNoise(boolean value) ;**
> **void setPhiNoise(boolean value) ;**
> **void setDistanceNoise(boolean value) ;**

Each time a point is acquired, a noise factor is added to the angle θ and or φ and or the hit distance when computing the point’s position. Noise on θ
and φ modifies the direction in which the point is thought to be ; noise on the
hit distance the distance (in this direction) from the scanner.

The type of noise can be set through the following methods :

> **void setThetaNoiseType(int type, boolean adapt, double param1,
double param2) ;**
> **void setPhiNoiseType(int type, boolean adapt, double param1,
double param2) ;**
> **void setDistanceNoiseType(int type, boolean adapt, double param1,
double param2) ;**

//type = 0// sets the noise to an uniform perturbation, //type = 1// to a gaussian
one (any other value inducing no noise at all). //adapt = false// produces a noise
with fixed parameters, whereas //adapt = true// produces a noise which parameters
depends on the real value (see below).

Given the real value $\alpha_{r}$ of one parameter (θ, φ or the hit distance), the
value used to compute the point’s position is $`\alpha_{r} = \alpha_{r} + \epsilon`$, where ϵ is the noise.
With U(a, b) denoting the uniform density on [a, b] (a < b), and N(μ, σ) the
gaussian density of mean μ and standard deviation σ, the perturbation ϵ has the
corresponding density :

{{:tutorials:scanner_table.png}}

==== Annexes ====

=== Spherical coordinate system ===

The spherical coordinate system is a 3d-coordinate system in which the position of a point is specified by two angular parameters θ and φ and the radial distance
//r//. Given a direct orthonormal basis $B_{0} = (\vec{x}, \vec{y}, \vec{z})$, and a fixed origin point
//O//, these parameters, for some point M(r, θ, φ), are defined as follow (see Fig.2
p.7) :

> $\theta = \widehat{\vec{x}, \vec{OP}}, \theta \in \left[0; 2\pi\right]$
> $\phi = \widehat{\vec{z}, \vec{OM}}, \phi \in \left[0; \pi\right]$
> r = OM


with //P// the orthogonal projection of //M// on the plane $(O, \vec{y}, \vec{z})$. Note that
only the two angular parameters θ and φ are needed to define a direction (see
Fig.2 p.7).

For each direction (θ, φ) a local direct orthonormal basis $B_{\theta, \phi} = (\vec{u_{r}}, \vec{u_{\phi}}, \vec{u_{\theta}})$
can be de defined, with :

{{:tutorials:scanner_eq.png}}

=== Cylindrical coordinate system ===

The cylindrical coordinate system is a 3d-coordinate system in which the position of a point is specified by one angular parameter θ, one distance _r_ and one height //z//. Given a direct orthonormal basis $B_{0} = (\vec{x}, \vec{y}, \vec{z})$, and a fixed origin
point //O//, these parameters, for some point //M (r, θ, z)//, are defined as follow (see
Fig.2 p.7)


> $\theta = \widehat{\vec{x}, \vec{OP}}, \theta \in \left[0; 2\pi\right]$
> //r = OM//
> $z = \vec{OM} · \vec{z}$


{{:tutorials:scanner_coordinate.png}}

** Figure 2: Spherical and Cylindrical coordinate system **


with P the orthogonal projection of M on the plane $(O, \vec{x}, \vec{y})$ (see Fig.2 p.7).

For each angle θ a local direct orthonormal basis $B_{\theta} = (\vec{u}, \vec{u_{\theta}}, \vec{z})$ can be de
defined, with :

{{:tutorials:scanner_eq2.png}}