/* $Id: quadric.c,v 1.1 1996/09/27 01:19:39 brianp Exp $ */

/*
 * Mesa 3-D graphics library
 * Version:  2.0
 * Copyright (C) 1995-1996  Brian Paul
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the Free
 * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */


/*
 * $Log: quadric.c,v $
 * Revision 1.1  1996/09/27 01:19:39  brianp
 * Initial revision
 *
 */


/* TODO:
 *   texture coordinate support
 *   flip normals according to orientation
 *   there's still some inside/outside orientation bugs in possibly all
 *     but the sphere function
 */


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "gluP.h"



#ifndef M_PI
#  define M_PI (3.1415926)
#endif


/*
 * Convert degrees to radians:
 */
#define DEG_TO_RAD(A)   ((A)*(M_PI/180.0))


/*
 * Sin and Cos for degree angles:
 */
#define SIND( A )   sin( (A)*(M_PI/180.0) )
#define COSD( A)    cos( (A)*(M_PI/180.0) )


/*
 * Texture coordinates if texture flag is set
 */
#define TXTR_COORD(x,y)    if (qobj->TextureFlag) glTexCoord2f(x,y);



struct GLUquadricObj {
	GLenum	DrawStyle;		/* GLU_FILL, LINE, SILHOUETTE, or POINT */
	GLenum Orientation;		/* GLU_INSIDE or GLU_OUTSIDE */
	GLboolean TextureFlag;		/* Generate texture coords? */
	GLenum Normals;		/* GLU_NONE, GLU_FLAT, or GLU_SMOOTH */
	void (*ErrorFunc)(GLenum err);	/* Error handler callback function */
};



/*
 * Process a GLU error.
 */
static void quadric_error( GLUquadricObj *qobj, GLenum error, const char *msg )
{
   /* Call the error call back function if any */
   if (qobj->ErrorFunc) {
      (*qobj->ErrorFunc)( error );
   }
   /* Print a message to stdout if MESA_DEBUG variable is defined */
   if (getenv("MESA_DEBUG")) {
      fprintf(stderr,"GLUError: %s: %s\n", gluErrorString(error), msg );
   }
}




GLUquadricObj *gluNewQuadric( void )
{
   GLUquadricObj *q;

   q = (GLUquadricObj *) malloc( sizeof(struct GLUquadricObj) );
   if (q) {
      q->DrawStyle = GLU_FILL;
      q->Orientation = GLU_OUTSIDE;
      q->TextureFlag = GL_FALSE;
      q->Normals = GLU_SMOOTH;
      q->ErrorFunc = NULL;
   }
   return q;
}



void gluDeleteQuadric( GLUquadricObj *state )
{
   if (state) {
      free( (void *) state );
   }
}



/*
 * Set the drawing style to be GLU_FILL, GLU_LINE, GLU_SILHOUETTE, or GLU_POINT.
 */
void gluQuadricDrawStyle( GLUquadricObj *quadObject, GLenum drawStyle )
{
   if (quadObject && (drawStyle==GLU_FILL || drawStyle==GLU_LINE
		   || drawStyle==GLU_SILHOUETTE || drawStyle==GLU_POINT)) {
      quadObject->DrawStyle = drawStyle;
   }
   else {
      quadric_error( quadObject, GLU_INVALID_ENUM, "qluQuadricDrawStyle" );
   }
}



/*
 * Set the orientation to GLU_INSIDE or GLU_OUTSIDE.
 */
void gluQuadricOrientation( GLUquadricObj *quadObject, GLenum orientation )
{
   if (quadObject && (orientation==GLU_INSIDE || orientation==GLU_OUTSIDE)) {
      quadObject->Orientation = orientation;
   }
   else {
      quadric_error( quadObject, GLU_INVALID_ENUM, "qluQuadricOrientation" );
   }
}



/*
 * Set the error handler callback function.
 */
void gluQuadricCallback( GLUquadricObj *qobj,
			 GLenum which, void (*fn)(GLenum) )
{
   if (qobj && which==GLU_ERROR) {
      qobj->ErrorFunc = fn;
   }
}


void gluQuadricNormals( GLUquadricObj *quadObject, GLenum normals )
{
   if (quadObject
         && (normals==GLU_NONE || normals==GLU_FLAT || normals==GLU_SMOOTH)) {
      quadObject->Normals = normals;
   }
}


void gluQuadricTexture( GLUquadricObj *quadObject,
		        GLboolean textureCoords )
{
   if (quadObject) {
      quadObject->TextureFlag = textureCoords;
   }
}




/*
 * Call glNormal3f after scaling normal to unit length.
 */
static void normal3f( GLfloat x, GLfloat y, GLfloat z )
{
   GLdouble mag;

   mag = sqrt( x*x + y*y + z*z );
   if (mag>0.00001F) {
      x /= mag;
      y /= mag;
      z /= mag;
   }
   glNormal3f( x, y, z );
}



void gluCylinder( GLUquadricObj *qobj,
                  GLdouble baseRadius, GLdouble topRadius, GLdouble height,
                  GLint slices, GLint stacks )
{
   GLdouble da, r, dr, dz;
   GLfloat x, y, z, nz, nsign;
   GLint i, j;

   if (qobj->Orientation==GLU_INSIDE) {
      nsign = -1.0;
   }
   else {
      nsign = 1.0;
   }

   da = 2.0*M_PI / slices;
   dr = (topRadius-baseRadius) / stacks;
   dz = height / stacks;
   nz = (baseRadius-topRadius) / height;  /* Z component of normal vectors */

   if (qobj->DrawStyle==GLU_POINT) {
      glBegin( GL_POINTS );
      for (i=0;i<slices;i++) {
	 x = cos(i*da);
	 y = sin(i*da);
	 normal3f( x*nsign, y*nsign, nz*nsign );

	 z = 0.0;
	 r = baseRadius;
	 for (j=0;j<=stacks;j++) {
	    glVertex3f( x*r, y*r, z );
	    z += dz;
	    r += dr;
	 }
      }
      glEnd();
   }
   else if (qobj->DrawStyle==GLU_LINE || qobj->DrawStyle==GLU_SILHOUETTE) {
      /* Draw rings */
      if (qobj->DrawStyle==GLU_LINE) {
	 z = 0.0;
	 r = baseRadius;
	 for (j=0;j<=stacks;j++) {
	    glBegin( GL_LINE_LOOP );
	    for (i=0;i<slices;i++) {
	       x = cos(i*da);
	       y = sin(i*da);
	       normal3f( x*nsign, y*nsign, nz*nsign );
	       glVertex3f( x*r, y*r, z );
	    }
	    glEnd();
	    z += dz;
	    r += dr;
	 }
      }
      else {
	 /* draw one ring at each end */
	 if (baseRadius!=0.0) {
	    glBegin( GL_LINE_LOOP );
	    for (i=0;i<slices;i++) {
	       x = cos(i*da);
	       y = sin(i*da);
	       normal3f( x*nsign, y*nsign, nz*nsign );
	       glVertex3f( x*baseRadius, y*baseRadius, 0.0 );
	    }
	    glEnd();
	    glBegin( GL_LINE_LOOP );
	    for (i=0;i<slices;i++) {
	       x = cos(i*da);
	       y = sin(i*da);
	       normal3f( x*nsign, y*nsign, nz*nsign );
	       glVertex3f( x*topRadius, y*topRadius, height );
	    }
	    glEnd();
	 }
      }
      /* draw length lines */
      glBegin( GL_LINES );
      for (i=0;i<slices;i++) {
	 x = cos(i*da);
	 y = sin(i*da);
	 normal3f( x*nsign, y*nsign, nz*nsign );
	 glVertex3f( x*baseRadius, y*baseRadius, 0.0 );
	 glVertex3f( x*topRadius, y*topRadius, height );
      }
      glEnd();
   }
   else if (qobj->DrawStyle==GLU_FILL) {
      GLfloat du = 1.0 / slices;
      GLfloat dv = 1.0 / stacks;
      GLfloat tcx = 0.0, tcy = 0.0;

      for (i=0;i<slices;i++) {
	 GLfloat x1 = -sin(i*da);
	 GLfloat y1 = cos(i*da);
	 GLfloat x2 = -sin((i+1)*da);
	 GLfloat y2 = cos((i+1)*da);
	 z = 0.0;
	 r = baseRadius;
	 tcy = 0.0;
	 glBegin( GL_QUAD_STRIP );
	 for (j=0;j<=stacks;j++) {
	    if (nsign==1.0) {
	       normal3f( x1*nsign, y1*nsign, nz*nsign );
	       TXTR_COORD(tcx, tcy);
	       glVertex3f( x1*r, y1*r, z );
	       normal3f( x2*nsign, y2*nsign, nz*nsign );
	       TXTR_COORD(tcx+du, tcy);
	       glVertex3f( x2*r, y2*r, z );
	    }
	    else {
	       normal3f( x2*nsign, y2*nsign, nz*nsign );
	       TXTR_COORD(tcx, tcy);
	       glVertex3f( x2*r, y2*r, z );
	       normal3f( x1*nsign, y1*nsign, nz*nsign );
	       TXTR_COORD(tcx+du, tcy);
	       glVertex3f( x1*r, y1*r, z );
	    }
	    z += dz;
	    r += dr;
	    tcy += dv;
	 }
	 glEnd();
	 tcx += du;
      }
   }
}





void gluSphere( GLUquadricObj *qobj,
                GLdouble radius, GLint slices, GLint stacks )
{
   GLfloat rho, drho, theta, dtheta;
   GLfloat x, y, z;
   GLfloat s, t, ds, dt;
   GLint i, j, imin, imax;
   GLboolean normals;
   GLfloat nsign;

   if (qobj->Normals==GLU_NONE) {
      normals = GL_FALSE;
   }
   else {
      normals = GL_TRUE;
   }
   if (qobj->Orientation==GLU_INSIDE) {
      nsign = -1.0;
   }
   else {
      nsign = 1.0;
   }

   drho = M_PI / (GLfloat) stacks;
   dtheta = 2.0 * M_PI / (GLfloat) slices;

   /* texturing: s goes from 0.0/0.25/0.5/0.75/1.0 at +y/+x/-y/-x/+y axis */
   /* t goes from -1.0/+1.0 at z = -radius/+radius (linear along longitudes) */
   /* cannot use triangle fan on texturing (s coord. at top/bottom tip varies) */

   if (qobj->DrawStyle==GLU_FILL) {
     if (!qobj->TextureFlag) {
      /* draw +Z end as a triangle fan */
      glBegin( GL_TRIANGLE_FAN );
      glNormal3f( 0.0, 0.0, 1.0 );
      TXTR_COORD(0.5,1.0);
      glVertex3f( 0.0, 0.0, nsign * radius );
      for (j=0;j<=slices;j++) {
	 theta = (j==slices) ? 0.0 : j * dtheta;
	 x = -sin(theta) * sin(drho);
	 y = cos(theta) * sin(drho);
	 z = nsign * cos(drho);
	 if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	 glVertex3f( x*radius, y*radius, z*radius );
      }
      glEnd();
     }

      ds = 1.0 / slices;
      dt = 1.0 / stacks;
      t = 1.0;  /* because loop now runs from 0 */
      if (qobj->TextureFlag) {
        imin = 0;
        imax = stacks;
      }
      else {
        imin = 1;
        imax = stacks-1;
      }

      /* draw intermediate stacks as quad strips */
      for (i=imin;i<imax;i++) {
	 rho = i * drho;
	 glBegin( GL_QUAD_STRIP );
         s = 0.0;
	 for (j=0;j<=slices;j++) {
	    theta = (j==slices) ? 0.0 : j * dtheta;
	    x = -sin(theta) * sin(rho);
	    y = cos(theta) * sin(rho);
	    z = nsign * cos(rho);
	    if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	    TXTR_COORD(s,t);
	    glVertex3f( x*radius, y*radius, z*radius );
	    x = -sin(theta) * sin(rho+drho);
	    y = cos(theta) * sin(rho+drho);
	    z = nsign * cos(rho+drho);
	    if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	    TXTR_COORD(s,t-dt);
            s += ds;
	    glVertex3f( x*radius, y*radius, z*radius );
	 }
	 glEnd();
	 t -= dt;
      }

     if (!qobj->TextureFlag) {
      /* draw -Z end as a triangle fan */
      glBegin( GL_TRIANGLE_FAN );
      glNormal3f( 0.0, 0.0, -1.0 );
      TXTR_COORD(0.5,0.0);
      glVertex3f( 0.0, 0.0, -radius*nsign );
      rho = M_PI - drho;
      s = 1.0;
      t = dt;
      for (j=slices;j>=0;j--) {
	 theta = (j==slices) ? 0.0 : j * dtheta;
	 x = -sin(theta) * sin(rho);
	 y = cos(theta) * sin(rho);
	 z = nsign * cos(rho);
	 if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	 TXTR_COORD(s,t);
         s -= ds;
	 glVertex3f( x*radius, y*radius, z*radius );
      }
      glEnd();
     }
   }
   else if (qobj->DrawStyle==GLU_LINE || qobj->DrawStyle==GLU_SILHOUETTE) {
      /* draw stack lines */
      for (i=1;i<stacks;i++) {  /* stack line at i==stacks-1 was missing here */
	 rho = i * drho;
	 glBegin( GL_LINE_LOOP );
	 for (j=0;j<slices;j++) {
	    theta = j * dtheta;
	    x = cos(theta) * sin(rho);
	    y = sin(theta) * sin(rho);
	    z = cos(rho);
	    if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	    glVertex3f( x*radius, y*radius, z*radius );
	 }
	 glEnd();
      }
      /* draw slice lines */
      for (j=0;j<slices;j++) {
	 theta = j * dtheta;
	 glBegin( GL_LINE_STRIP );
	 for (i=0;i<=stacks;i++) {
	    rho = i * drho;
	    x = cos(theta) * sin(rho);
	    y = sin(theta) * sin(rho);
	    z = cos(rho);
	    if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	    glVertex3f( x*radius, y*radius, z*radius );
	 }
	 glEnd();
      }
   }
   else if (qobj->DrawStyle==GLU_POINT) {
      /* top and bottom-most points */
      glBegin( GL_POINTS );
      if (normals)  glNormal3f( 0.0, 0.0, nsign );
      glVertex3d( 0.0, 0.0, radius );
      if (normals)  glNormal3f( 0.0, 0.0, -nsign );
      glVertex3d( 0.0, 0.0, -radius );

      /* loop over stacks */
      for (i=1;i<stacks-1;i++) {
	 rho = i * drho;
	 for (j=0;j<slices;j++) {
	    theta = j * dtheta;
	    x = cos(theta) * sin(rho);
	    y = sin(theta) * sin(rho);
	    z = cos(rho);
	    if (normals)  glNormal3f( x*nsign, y*nsign, z*nsign );
	    glVertex3f( x*radius, y*radius, z*radius );
	 }
      }
      glEnd();
   }

}



void gluDisk( GLUquadricObj *qobj,
              GLdouble innerRadius, GLdouble outerRadius,
              GLint slices, GLint loops )
{
   GLdouble a, da;
   GLfloat r, dr;
   GLfloat x, y;
   GLfloat r1, r2, dtc;
   GLint s, l;

   /* Normal vectors */
   if (qobj->Normals!=GLU_NONE) {
      if (qobj->Orientation==GLU_OUTSIDE) {
	 glNormal3f( 0.0, 0.0, +1.0 );
      }
      else {
	 glNormal3f( 0.0, 0.0, -1.0 );
      }
   }

   da = 2.0*M_PI / slices;
   dr = (outerRadius-innerRadius) / (GLfloat) loops;

   /* texture of a gluDisk is a cut out of the texture unit square */
   /* x, y in [-outerRadius, +outerRadius]; s, t in [0, 1] (linear mapping) */
   dtc = 2.0f * outerRadius;

   switch (qobj->DrawStyle) {
      case GLU_FILL:
	 {
         GLfloat sa,ca;
         r1 = innerRadius;
         for (l=0;l<loops;l++) {
	    r2 = r1 + dr;
	    if (qobj->Orientation==GLU_OUTSIDE) {
	       glBegin( GL_QUAD_STRIP );
	       for (s=0;s<=slices;s++) {
		  if (s==slices) a = 0.0;
		  else  a = s * da;
		  sa = sin(a); ca = cos(a);
                  TXTR_COORD(0.5+sa*r2/dtc,0.5+ca*r2/dtc);
                  glVertex2f( r2*sa, r2*ca );
                  TXTR_COORD(0.5+sa*r1/dtc,0.5+ca*r1/dtc);
                  glVertex2f( r1*sa, r1*ca );
	       }
	       glEnd();
	    }
	    else {
	       glBegin( GL_QUAD_STRIP );
	       for (s=slices;s>=0;s--) {
		  if (s==slices) a = 0.0;
		  else  a = s * da;
		  sa = sin(a); ca = cos(a);
                  TXTR_COORD(0.5-sa*r2/dtc,0.5+ca*r2/dtc);
                  glVertex2f( r2*sa, r2*ca );
                  TXTR_COORD(0.5-sa*r1/dtc,0.5+ca*r1/dtc);
                  glVertex2f( r1*sa, r1*ca );
	       }
	       glEnd();
	    }
	    r1 = r2;
	 }
         }
         break;
      case GLU_LINE:
	 /* draw rings */
	 for (r=innerRadius; r<=outerRadius; r+=dr) {
	    glBegin( GL_LINE_LOOP );
	    for (a=0.0; a<2.0*M_PI; a+=da) {
	       glVertex2f( r*sin(a), r*cos(a) );
	    }
	    glEnd();
	 }
	 /* draw spokes */
	 for (a=0.0; a<2.0*M_PI; a+=da) {
	    x = sin(a);
	    y = cos(a);
	    glBegin( GL_LINE_STRIP );
	    for (r=innerRadius; r<=outerRadius; r+=dr) {
	       glVertex2f( r*x, r*y );
	    }
	    glEnd();
	 }
	 break;
      case GLU_POINT:
	 glBegin( GL_POINTS );
	 for (a=0.0; a<2.0*M_PI; a+=da) {
	    x = sin(a);
	    y = cos(a);
	    for (r=innerRadius; r<=outerRadius; r+=dr) {
	       glVertex2f( r*x, r*y );
	    }
	 }
	 glEnd();
	 break;
      case GLU_SILHOUETTE:
	 if (innerRadius!=0.0) {
	    glBegin( GL_LINE_LOOP );
	    for (a=0.0; a<2.0*M_PI; a+=da) {
	       x = innerRadius * sin(a);
	       y = innerRadius * cos(a);
	       glVertex2f( x, y );
	    }
	    glEnd();
	 }
	 glBegin( GL_LINE_LOOP );
	 for (a=0; a<2.0*M_PI; a+=da) {
	    x = outerRadius * sin(a);
	    y = outerRadius * cos(a);
	    glVertex2f( x, y );
	 }
	 glEnd();
	 break;
      default:
         abort();
   }
}



void gluPartialDisk( GLUquadricObj *qobj, GLdouble innerRadius,
		     GLdouble outerRadius, GLint slices, GLint loops,
		     GLdouble startAngle, GLdouble sweepAngle )
{
   if (qobj->Normals!=GLU_NONE) {
      if (qobj->Orientation==GLU_OUTSIDE) {
	 glNormal3f( 0.0, 0.0, +1.0 );
      }
      else {
	 glNormal3f( 0.0, 0.0, -1.0 );
      }
   }

   if (qobj->DrawStyle==GLU_POINT) {
      GLint loop, slice;
      GLdouble radius, delta_radius;
      GLdouble angle, delta_angle;
      delta_radius = (outerRadius - innerRadius) / (loops-1);
      delta_angle = DEG_TO_RAD((sweepAngle) / (slices-1));
      glBegin( GL_POINTS );
      radius = innerRadius;
      for (loop=0; loop<loops; loop++) {
	 angle = DEG_TO_RAD(startAngle);
	 for (slice=0; slice<slices; slice++) {
	    glVertex2d( radius * sin(angle), radius * cos(angle) );
	    angle += delta_angle;
	 }
	 radius += delta_radius;
      }
      glEnd();
   }
   else if (qobj->DrawStyle==GLU_LINE) {
      GLint loop, slice;
      GLdouble radius, delta_radius;
      GLdouble angle, delta_angle;
      delta_radius = (outerRadius - innerRadius) / (loops-1);
      delta_angle = DEG_TO_RAD((sweepAngle) / (slices-1));
      /* draw rings */
      radius = innerRadius;
      for (loop=0; loop<loops; loop++) {
	 angle = DEG_TO_RAD(startAngle);
	 glBegin( GL_LINE_STRIP );
	 for (slice=0; slice<slices; slice++) {
	    glVertex2d( radius * sin(angle), radius * cos(angle) );
	    angle += delta_angle;
	 }
	 glEnd();
	 radius += delta_radius;
      }
      /* draw spokes */
      angle = DEG_TO_RAD(startAngle);
      for (slice=0; slice<slices; slice++) {
	 radius = innerRadius;
	 glBegin( GL_LINE_STRIP );
	 for (loop=0; loop<loops; loop++) {
	    glVertex2d( radius * sin(angle), radius * cos(angle) );
	    radius += delta_radius;
	 }
	 glEnd();
	 angle += delta_angle;
      }
   }
   else if (qobj->DrawStyle==GLU_SILHOUETTE) {
      GLint slice;
      GLdouble angle, delta_angle;
      delta_angle = DEG_TO_RAD((sweepAngle) / (slices-1));
      /* draw outer ring */
      glBegin( GL_LINE_STRIP );
      angle = DEG_TO_RAD(startAngle);
      for (slice=0; slice<slices; slice++) {
	 glVertex2d( outerRadius * sin(angle), outerRadius * cos(angle) );
	 angle += delta_angle;
      }
      glEnd();
      /* draw inner ring */
      if (innerRadius>0.0) {
	 glBegin( GL_LINE_STRIP );
	 angle = DEG_TO_RAD(startAngle);
	 for (slice=0; slice<slices; slice++) {
	    glVertex2d( innerRadius * sin(angle), innerRadius * cos(angle) );
	    angle += delta_angle;
	 }
	 glEnd();
      }
      /* draw spokes */
      if (sweepAngle<360.0) {
	 GLdouble stopAngle = startAngle + sweepAngle;
	 glBegin( GL_LINES );
	 glVertex2d( innerRadius*SIND(startAngle), innerRadius*COSD(startAngle) );
	 glVertex2d( outerRadius*SIND(startAngle), outerRadius*COSD(startAngle) );
	 glVertex2d( innerRadius*SIND(stopAngle), innerRadius*COSD(stopAngle) );
	 glVertex2d( outerRadius*SIND(stopAngle), outerRadius*COSD(stopAngle) );
	 glEnd();
      }
   }
   else if (qobj->DrawStyle==GLU_FILL) {
      GLint loop, slice;
      GLdouble radius, delta_radius;
      GLdouble angle, delta_angle;
      delta_radius = (outerRadius - innerRadius) / (loops-1);
      delta_angle = DEG_TO_RAD((sweepAngle) / (slices-1));
      radius = innerRadius;
      for (loop=0; loop<loops-1; loop++) {
	 glBegin( GL_QUAD_STRIP );
	 angle = DEG_TO_RAD(startAngle);
	 for (slice=0; slice<slices; slice++) {
	    if (qobj->Orientation==GLU_OUTSIDE) {
	       glVertex2d( (radius+delta_radius)*sin(angle),
			   (radius+delta_radius)*cos(angle) );
	       glVertex2d( radius * sin(angle), radius * cos(angle) );
	    }
	    else {
	       glVertex2d( radius * sin(angle), radius * cos(angle) );
	       glVertex2d( (radius+delta_radius)*sin(angle),
			   (radius+delta_radius)*cos(angle) );
	    }
	    angle += delta_angle;
	 }
	 glEnd();
	 radius += delta_radius;
      }
   }
}



