Public class Projection

Syntax
public abstract class Projection extends Jcalmcomp

Description
Projection class is 3D drawing tool in engineering usage which is extended from Jcalcomp.
It provides 3D vector and tensor treatment of graphics.
Projection is extended from Jcalcomp class and user should make thier own class extended from Projection .

MEMBER SUMMARY

void Projection()

PURPOSE :
Open world coordinate system to make relation with projection system(user's coordinate)
Almost all parameters are common with the constructor of Jcalmcomp

SYNTAX :
public Projection(int x_dim,int y_dim, double wid, double gx01,double gy01, long jgx0,long jgy0, long jgx1,long jgy1)
public Projection(int x_dim,int y_dim, double wid, double gx01,double gy01)
public Projection()
public Projection(int x_dim,int y_dim)
public Projection(int x_dim,int y_dim,double wid)

DESCRIPTION : The projection operation is controlled by bprep(), while projection plane is fixed by this constructor. Users have to call bprep() after construction method.

PARAMETERS :
parent constructor is called and see Jcalcomp(). Only default values are presented here.

RETURNS : none

SEEALSO : Jcalcomp(),bprep()

EXAMPLE :see example of pplot()

void bprep()

PURPOSE :
Fix view port(projection plane) and scaling related to 3D coordinates.

SYNTAX :
void bprep(int ang,int idf, double h1d,double h2d,double h3d, double phaid,double psaid,
double cvdd, double x,double y,double z)

DESCRIPTION :
This Projection class has the perspective and isometric mode. They are controlled by variable ang.
In case of perspective view, the eye point is needed, which is decided by the distance cvd (Clear View Distance) vertically behind the origin on projection plane. The view port has 5 degrees of freedom.
2 of them are rotating angle around y axis and z axis sequentially. and parallel movement defined by (x,y,z). Initially, the view port is placed vertically to x axis , and 20.0 distance from 3D origin. For Isometric view, the view port is rotated twice, and then moved in parallel. For perspective view the eye is moved with the plane, keeping cvd distance.

PARAMETERS :

RETURNS : none

SEEALSO : Projection()

EXAMPLE :see example of pplot()
import java.applet.*;
import java.awt.*;

//******************************************
public class Fig007 extends Projection
//******************************************
{
//==========================================
public Fig007()
//==========================================
{
super(500,400,30.,-16.,-5.5,0,0,300,300);
}
//==========================================
public void paint( Graphics g )
//==========================================
{
int i,j;
double n=30.,m=60.;

bprep(1,3,
   0.,0.,0.,
   90.- m,-180.+n,
   25.,
   0.,0.,0.);

g.setColor(Color.black);
paxis(g,-al,-al,0.,1.,2.*al,0.,90.,0.,"X",1,1,5,-2.,1.);
pplot(g,-al,+al,-al+al,3);pplot(g,al,+al,-al+al,2);
pplot(g,-al,-al,+al+al,3);pplot(g,al,-al,+al+al,2);
pplot(g,-al,+al,+al+al,3);pplot(g,al,+al,+al+al,2);
pplot(g,-al,-al,-al+al,3);pplot(g,al,-al,-al+al,2);

g.setColor(Color.green);
paxis(g,-al,-al,0.,-1.,2.*al,0.,0.,90.,"Y",1,1,5,-2.,1.);
pplot(g,-al,-al,-al+al,3);pplot(g,-al,+al,-al+al,2);
pplot(g,+al,-al,-al+al,3);pplot(g,+al,+al,-al+al,2);
pplot(g,+al,-al,+al+al,3);pplot(g,+al,+al,+al+al,2);
pplot(g,-al,-al,+al+al,3);pplot(g,-al,+al,+al+al,2);

g.setColor(Color.red);
paxis(g,-al,-al,0.,-1.,2.*al,90.,-90.,180.,"Z",1,1,5,0.,1.);
pplot(g,-al,+al,-al+al,3);pplot(g,-al,+al,al+al,2);
pplot(g,+al,-al,-al+al,3);pplot(g,+al,-al,al+al,2);
pplot(g,+al,+al,-al+al,3);pplot(g,+al,+al,al+al,2);
pplot(g,-al,-al,-al+al,3);pplot(g,-al,-al,al+al,2);

g.setColor((Color.blue));

Vector
   V0=new Vector(-al-10.,0.,0.),
   V1=new Vector(0.,5.,0.),
   V2=new Vector(0.,0.,5.);
g.setColor(Color.blue);
for(double phai=0.;phai<=60.;phai+=20.)
{
   Trape( g,V0,V1,V2,phai,0.);
}
g.setColor(Color.red);
for(double psai=0.;psai<=80.;psai+=20.)
{
   Trape( g,V0,V1,V2,60.,psai);
}

}

//==========================================
public void Trape( Graphics g,
   Vector V0, Vector V1, Vector V2,
   double phai, double psai)
//==========================================
{
   Tensor E=new Tensor(1.);
   Vector
    Origin = new Vector(),
    W1 = new Vector(V0.Plus(V1.Plus(V2))),
    W2 = new Vector(V0.Plus(V1.Minus(V2))),
    W3 = new Vector(V0.Minus(V1.Plus(V2))),
    W4 = new Vector(V0.Minus(V1.Minus(V2)));

E.Z_Rotate(psai);

   E.Y_Rotate(phai);

   Vector
    A0 = new Vector(E.Mult(V0)),
    A1 = new Vector(E.Mult(W1)),
    A2 = new Vector(E.Mult(W2)),
    A3 = new Vector(E.Mult(W3)),
    A4 = new Vector(E.Mult(W4));

   pplot(g,Origin,3);
   pplot(g,A0,2);
   psymbol(g,A2.Get_Elem(0),
    A2.Get_Elem(1),
    A2.Get_Elem(2),
    0.,90.-phai,psai-90.,1.5,"Java",4);

   pplot(g,A1,3);
   pplot(g,A2,2);
   pplot(g,A3,2);
   pplot(g,A4,2);
   pplot(g,A1,2);

}
}

void pplot()

PURPOSE :

The most basic method for 3D plotting. This method traces movement of drawing pen, which is anlogous to u_plot() in Jcalcomp.
SYNTAX :
void pplot(Graphics g,double x,double y,double z,int n)

DESCRIPTION :
3D lines are projected to the projection plane.

PARAMETERS :

RETURNS : none

SEEALSO : Projection(),bprep(),Jcalcomp.lline()

EXAMPLE :
import java.applet.*;
import java.awt.*;

//******************************************
public class Fig006 extends Projection
//******************************************
{
//==========================================
public Fig006()
//==========================================
{
super(500,400,30.,-16.,-5.5,0,0,300,300);
}
//==========================================
public void paint( Graphics g )
//==========================================
{
int i,j;
double n=30.,m=60.;

bprep(1,3,
   0.,0.,0.,
   90.- m,-180.+n,
   25.,
   0.,0.,0.);
// Base square
g.setColor(Color.black);
paxis(g,-al,-al,0.,1.,2.*al,0.,90.,0.,"X",1,1,5,0.,1.);
pplot(g,-al,+al,-al+al,3);pplot(g,al,+al,-al+al,2);
pplot(g,-al,-al,+al+al,3);pplot(g,al,-al,+al+al,2);
pplot(g,-al,+al,+al+al,3);pplot(g,al,+al,+al+al,2);
pplot(g,-al,-al,-al+al,3);pplot(g,al,-al,-al+al,2);

g.setColor(Color.green);
paxis(g,-al,-al,0.,-1.,2.*al,0.,0.,90.,"Y",1,1,5,0.,1.);
pplot(g,-al,-al,-al+al,3);pplot(g,-al,+al,-al+al,2);
pplot(g,+al,-al,-al+al,3);pplot(g,+al,+al,-al+al,2);
pplot(g,+al,-al,+al+al,3);pplot(g,+al,+al,+al+al,2);
pplot(g,-al,-al,+al+al,3);pplot(g,-al,+al,+al+al,2);

g.setColor((Color.blue));
for(double latitude=-90.;latitude<90.;latitude+=10.)
{
pplot(g,al*Math.cos(latitude*DPAI),0.,al*Math.sin(latitude*DPAI)+al,3);
for(double longitude=0.;longitude<=360.;longitude+=10.)
{
   double xx=al*Math.cos(latitude*DPAI)*Math.cos(longitude*DPAI);
   double yy=al*Math.cos(latitude*DPAI)*Math.sin(longitude*DPAI);
   pplot(g,xx,yy,al*Math.sin(latitude*DPAI)+al,2);
}
}
for(double longitude=0.;longitude<=360.;longitude+=10.)
{
pplot(g,0,0.,al+al,3);
for(double latitude=-90.;latitude<90.;latitude+=10.)
{
   double xx=al*Math.cos(latitude*DPAI)*Math.cos(longitude*DPAI);
   double yy=al*Math.cos(latitude*DPAI)*Math.sin(longitude*DPAI);
   pplot(g,xx,yy,al*Math.sin(latitude*DPAI)+al,2);
}
}

}
}

void pcontor()

PURPOSE :
Draw 3D graph in wire frame and surface model.
SYNTAX :
void p_contor(Graphics g,double x0,double y0,double z0, double xwid,double ywid, int imax,int jmax)

DESCRIPTION :
This method is logically different from contour method in Jcalcomp. Ths is mainly for Cartesian mesh system, which is located in x-y plane. The value of z component is given by double func(double x,double y) which can be overridden by user.

PARAMETERS :
            g
            x0            x componet of the origin of 3D contour
            y0            y componet of the origin of 3D contour
            z0            z componet of the origin of 3D contour
            xwid        dimension of 3D contour in x direction( world coordinate)
            ywid        dimension of 3D contour in y direction( world coordinate)
            imax        mesh size in x direction
            jmax        mesh size in y direction

<> surface

RETURNS : none

SEEALSO : bprep()

EXAMPLE :

void psymbol()

PURPOSE :
Draw symbols and strings in arbitrary direction and height (Vector font)
SYNTAX :
void psymbol(Graphics g,
    double x,double y,double z,
    double dphai,double dtheta,double dpsai,
    double height,
    String text,int in)

DESCRIPTION :

PARAMETERS :
            g
            x            Starting point of string. The x coordinate of Left bottom corner of the first charcter.
             y            Starting point of string. The y coordinate of Left bottom corner of the first charcter.
               z            Starting point of string. The z coordinate of Left bottom corner of the first charcter.
           dphai                  The angle of string in degree from horizontal left to right direction.
            dtheta
            dpsai,
            height        The height of characters.
            text        String to be paint. If the 1st syntax is applied, Vector font is chosen.
                   If 2nd, the current system font is chosen which is horizontal only.
            in        The number of charactors in the string.
RETURNS : none

SEEALSO : bprep(),paxis(),plgaxis(),pnumber(),Jcalcomp.symbol()

EXAMPLE :

import java.applet.*;
import java.awt.*;

//******************************************
public class Fig008 extends Projection
//******************************************
{
//==========================================
public Fig008()
//==========================================
{
super(500,400,30.,-16.,-5.5,0,0,300,300);
}
//==========================================
public void paint( Graphics g )
//==========================================
{
int i,j;
double n=30.,m=60.;

bprep(1,3,
   0.,0.,0.,
   90.- m,-180.+n,
   25.,
   0.,0.,0.);
// Base square
g.setColor(Color.black);
paxis(g,-al,-al,0.,1.,2.*al,0.,90.,0.,"X",1,1,5,-2.,1.);
pplot(g,-al,+al,-al+al,3);pplot(g,al,+al,-al+al,2);
pplot(g,-al,-al,+al+al,3);pplot(g,al,-al,+al+al,2);
pplot(g,-al,+al,+al+al,3);pplot(g,al,+al,+al+al,2);
pplot(g,-al,-al,-al+al,3);pplot(g,al,-al,-al+al,2);

g.setColor((Color.blue));

g.setColor(Color.black);
psymbol(g,0.,0.,0.,0.,0.,0.,4.,"ABV",3);
g.setColor(Color.red);
psymbol(g,0.,0.,0.,90.,0.,0.,4.,"ABV",3);
g.setColor(Color.green);
psymbol(g,0.,0.,0.,0.,45.,-90.,4.,"ABV",3);
g.setColor(Color.blue);
psymbol(g,0.,0.,0.,45.,0.,-90.,4.,"ABV",3);
}

}

void pnumber()

PURPOSE :
Draw number of double in arbitrary direction and height (Vector font).The style of presentation can be specified.
SYNTAX :
void pnumber(Graphics g,
    double x,double y,double z,double h,
    double dphai,double dtheta,double dpsai,
    double fpn,int n)

DESCRIPTION :

PARAMETERS :
            g
            x           Starting point of number. The x coordinate of Left bottom corner of the first charcter.
            y            Starting point of number. The y coordinate of Left bottom corner of the first charcter.
            z             Starting point of number. The zcoordinate of Left bottom corner of the first charcter.
            h            The height of characters.
            dphai
            dtheta
            dpsai
            fpn        The objective double number.
            n            The column under decimal point. It n<0, the number is rounded by n power of 10.

RETURNS : none

SEEALSO : psymbol(),plgaxis(),Jcalcomp.number()

EXAMPLE :

void plgaxis()

PURPOSE :
User can draw logarithm plotting lines, and its axis for the benifit of recognition.
SYNTAX :
void plgaxis(Graphics g, double x,double y,double z,double t,
double dphai,double dtheta,double dpsai, int isep,String text,int in,int m)
DESCRIPTION :
User has to recognize 3D system applying "world coordinate" here. This lgaxis method is the interface of them. x, y, z and t are in world coordinate system,
and 10**m and 10**(m+isep) are in User logarithm Coordinate system.

PARAMETERS :
            g
            x            Starting point x coordinate(in World Coodinate system)
            y            Starting point y coordinate(in World Coodinate system)
            z            Starting point z coordinate(in World Coodinate system)
            t             lemgth of lgaxis(in World Coodinate system)
            dphai
            dtheta
            dpsai
            isep        Abs(isep) is number of power to be developed in t. If isept>0, axis is drawn in the direction of clockwise. If isep<0, counter-clockwise.
            text        Title string. It is located at the place specified by t and isep.
            in            length of title string
            m        starting power

RETURNS : none

SEEALSO : bprep()

EXAMPLE :

void paxis()

PURPOSE :User can draw 3D plotting lines, and its axis for the benifit of recognition.

SYNTAX :
void paxis(Graphics g,
    double x,double y,double z,double d,double t,
    double dphai,double dtheta,double dpsai,
     String text,int in,int m,int md,
     double sm,double smd)
DESCRIPTION :
paxis provide arbitrary location of axis, which include it rotation.
User have to recognize 3D system applying "world coordinate" here.
This axis method is the interface of them. x0, y0, d, and t are in world coordinate system,
and
sm and smd are in User Coordinate system.
PARAMETERS :
            g
            x            Starting point x coordinate(in World Coodinate system)
            y            Starting point y coordinate(in World Coodinate system)
            z            Starting point z coordinate(in World Coodinate system)
            d            length of axix (in World Coodinate system)
             t            Abs(t) is length and increment of supplemental line. If t>0, axis is drawn in the direction
     of clockwise.                 If t<0, counter-clockwise.
            dphai
            dtheta
            dpsai
            text         Title string. It is located at the place specified by t.
            in            number of characters of text
            m            initial position to print value
            md           increment of supplemental line
          sm            starting value printed
         smd            increment of printed value

RETURNS : none

SEEALSO : bprep()

EXAMPLE : see example of bprep()

double RayTrace()

PURPOSE :By given surface and light source, user can get the brightness of the surface element by the cosine of the reflection ray on the surface element and the projection line. User have to control the color specification corresponding brightness by the value.
This algorithm is simple and then care neither shadows nor refllections from wall or other object's surface.
SYNTAX :
double RayTrace(Graphics g,Vector m,Vector s1,Vector s2,Vector r)

DESCRIPTION :
The allocation vector m identifies the coordinate of objective surface. Vector s1 and s2 is unit vector on the surface, which are linear independent. The vector r is light source unit vector.
The surface element have outer and inner surface, which is decided by the sequence of s1 and s2.
The right screw method is applied here. The vector product of these two vectors makes a vertical unit vector, in which direction of "+" is outer surface. When two same surface elements are given at the same coordinate, if the sequence of s1 and s2 is inverse in calling method, the brightnesses have different sign "+" and "-".
PARAMETERS :
            g
            m        The location of the surface element.
            s1        Unit vector. One of independent vector on the surface
            s2        Unit vector. Another of independent vaector on the surface
            r          Unit vector. The light source vector.
RETURNS : double

SEEALSO : bprep()

EXAMPLE : :

import java.applet.*;
import java.awt.*;

//******************************************
public class Fig009 extends Projection
//******************************************
{
//==========================================
public Fig009()
//==========================================
{
super(500,400,30.,-16.,-5.5,0,0,300,300);
}
//==========================================
public void paint( Graphics g )
//==========================================
{
g.drawString("Fig009:Jcalcomp",0,10);

int i,j;
double n=70.,m=30.;

bprep(0,3,
   0.,0.,0.,
   90.- m,-180.+n,
   25.,
   0.,0.,0.);
// Base square
g.setColor(Color.black);
paxis(g,-al,-al,0.,1.,2.*al,0.,90.,0.,"X",1,1,5,0.,1.);
pplot(g,-al,+al,-al+al,3);pplot(g,al,+al,-al+al,2);
pplot(g,-al,-al,+al+al,3);pplot(g,al,-al,+al+al,2);
pplot(g,-al,+al,+al+al,3);pplot(g,al,+al,+al+al,2);
pplot(g,-al,-al,-al+al,3);pplot(g,al,-al,-al+al,2);

g.setColor(Color.blue);
paxis(g,-al,-al,0.,-1.,2.*al,90.,-90.,180.,"Z",1,1,5,0.,1.);
pplot(g,-al,+al,-al+al,3);pplot(g,-al,+al,al+al,2);
pplot(g,+al,-al,-al+al,3);pplot(g,+al,-al,al+al,2);
pplot(g,+al,+al,-al+al,3);pplot(g,+al,+al,al+al,2);
pplot(g,-al,-al,-al+al,3);pplot(g,-al,-al,al+al,2);

g.setColor((Color.blue));
double Dlongi=10.,Dlatit=10.;
Vector rr=(new Vector(-2.,2.,-1.)).Unit();
Vector vv[]=new Vector[5];
for(double latitude=-90.;latitude<50.;latitude+=Dlatit)
{
for(double longitude=0.;longitude<=360.;longitude+=Dlongi)
{
   Vector m0=new Vector(
    al*Math.cos(latitude*DPAI)*Math.cos(longitude*DPAI),
    al*Math.cos(latitude*DPAI)*Math.sin(longitude*DPAI),
    al*Math.sin(latitude*DPAI)+al);

   Vector m1=new Vector(
    al*Math.cos((latitude+Dlatit)*DPAI)*Math.cos(longitude*DPAI),
    al*Math.cos((latitude+Dlatit)*DPAI)*Math.sin(longitude*DPAI),
    al*Math.sin((latitude+Dlatit)*DPAI)+al);
   Vector m2=new Vector(
    al*Math.cos(latitude*DPAI)*Math.cos((longitude+Dlongi)*DPAI),
    al*Math.cos(latitude*DPAI)*Math.sin((longitude+Dlongi)*DPAI),
    al*Math.sin(latitude*DPAI)+al);
   Vector m3=new Vector(
    al*Math.cos((latitude+Dlatit)*DPAI)*Math.cos((longitude+Dlongi)*DPAI),
    al*Math.cos((latitude+Dlatit)*DPAI)*Math.sin((longitude+Dlongi)*DPAI),
    al*Math.sin((latitude+Dlatit)*DPAI)+al);
   double Bright=RayTrace(g,m0,(m1.Minus(m0)).Unit(),(m2.Minus(m0)).Unit(),rr);
   vv[0]=m0;vv[1]=m1;vv[2]=m3;vv[3]=m2;
   if (Bright >1.)
    Poly3DPaint(g,new Color((float)((Bright+1.)/2.),(float)((Bright+1.)/2.),(float)((Bright+1.)/2.)),vv,4);
   else
    Poly3DPaint(g,new Color((float)((Bright+1.)/2.),(float)0.,(float)0.),vv,4);

}
}
pplot(g,new Vector(.5*al,-al,2.0*al),3);
pplot(g,(rr.Mult(2.)).Plus((new Vector(.5*al,-al
,2.0*al))),2);

g.setColor(Color.black);
pplot(g,-al,-al,+al+al,3);pplot(g,al,-al,+al+al,2);
g.setColor(Color.green);
pplot(g,-al,-al,+al+al,3);pplot(g,-al,+al,+al+al,2);
g.setColor(Color.blue);
paxis(g,-al,-al,0.,-1.,2.*al,90.,-90.,180.,"Z",1,1,5,0.,1.);
}
}

void Poly3DPaint()

PURPOSE :Paint 3D polygon in arbitrary Color.
The number of the vertex of polygons is under 5.

SYNTAX :
void Poly3DPaint(Graphics g,Color Ucolor,Vector[] v,int n)

DESCRIPTION :

PARAMETERS :
            g
            Ucolor        user giving color specification
            v                Array of 3D vector.
            n                Number of vertex. Under 5.
RETURNS : none

SEEALSO : RayTrace(),bprep(),Vector class

EXAMPLE : see example of RayTrace()

Public class Projection

MEMBER SUMMARY

Constructors & Destructors

3D Drawing Methods

3D Contour Line Drawing Methods

void Projection()

void bprep()

void pplot()

PURPOSE :

void pcontor()

void psymbol()

void pnumber()

void plgaxis()

void paxis()

double RayTrace()

void Poly3DPaint()