OpenGL/GLUT Incorrect lighting for GL_LINES - c

Question

I am asked to make a simple carousel that rotates by right and left click of mouse. For the sticks I used GL_LINES and the problem I am having is that there is no way to define normal vector or something similar as I did with GL_POLYGON to make the lighting be correct. I searched the web and I didn't find any source explaining the lighting for the GL_LINES (some people told me the lighting is automatic and I don't need to specify anything for GL_LINES), that is why I asked the questions.
Here is the screenshot of the front which show everything is fine from front:
Here is the screenshot of the back that shows the problems in lighting. In particular, the light source is in the back but still those sticks are bright.
Here is the another screenshot of the back that show the problems in lighting as well.
These are the two functions that specify horizontal and vertical sticks:
void DrawHorizontalStick(){
glLineWidth(15);
glColor3f(1.0, 0.0, 0.0);
glBegin(GL_LINES);
glVertex3f(0.0, 7.0, 0.0);
glVertex3f(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE), 0.0);
glEnd();
}
void DrawVerticalStick(){
glLineWidth(5);
glColor3f(1.0, 0.0, 0.0);
glBegin(GL_LINES);
glVertex3f(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE), 0.0);
glVertex3f(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE) - 1, 0.0);
glEnd();
}
Here is the complete source code:
#include <GL/glut.h>
#include <stdlib.h>
#include <Windows.h>
#include <math.h>
#include <stdio.h>
#define PI 3.14159265
#define numberOfRotationTypes 3
static GLfloat lpos[] = { 0.0, 6.0, 8.0, 1.0 };
static GLfloat black[] = { 0.0, 0.0, 0.0, 1.0 };
static GLfloat white[] = { 1.0, 1.0, 1.0, 1.0 };
static GLfloat red[] = { 1.0, 0.0, 0.0, 1.0 };
static GLfloat green[] = { 0.0, 1.0, 0.0, 1.0 };
static GLfloat blue[] = { 0.0, 0.0, 1.0, 1.0 };
static GLfloat yellow[] = { 1.0, 1.0, 0.0, 1.0 };
static GLfloat magenta[] = { 1.0, 0.0, 1.0, 1.0 };
static GLfloat cyan[] = { 0.0, 1.0, 1.0, 1.0 };
static GLfloat lightgreen[] = { 0.5, 1.0, 0.5, 1.0 };
static float alpha = 0.0;
static float beta = PI / 6.0;
static float zoom = 25.0;
static bool lightSource = true;
float numberOfTriangles = 1;
static GLdouble cpos[3];
static double fenceHeight = -0.5;
static int angle = 0;
static int angle__IN_RANGE = 0.0;
static double radian__IN_RANGE = 0.0;
static int arrayOfAnglesInRange[181];
static int id = 0;
static int speed = 0;
static int signal = 1;
static GLint window[2];
static int rotationType = 0;
void init(void)
{
glClearColor(0.0, 0.0, 0.0, 0.0);
glEnable(GL_DEPTH_TEST);
glShadeModel(GL_SMOOTH);
/* since back "face" appears in wireframe mode */
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
}
void writemessage()
{
}
void processAngle(){
angle__IN_RANGE = arrayOfAnglesInRange[abs(angle) % 181];
}
void setRadian_IN_RANGE(){
radian__IN_RANGE = ((float)angle__IN_RANGE / 180) * PI;
}
void fillArray(){
int j = -45;
for (int i = 0; i < 181; i++)
{
if (i < 90)
arrayOfAnglesInRange[i] = j++;
else
arrayOfAnglesInRange[i] = j--;
}
//for (int i = 0; i < 182; i++)
//{
// printf("%d\n", arrayOfAnglesInRange[i]);
//}
}
void keepTrackOfID(){
int tempAngle = angle;
if (id % 4 == 0)
angle += 0;
else if (id % 4 == 1)
angle += 30;
else if (id % 4 == 2)
angle += 60;
else if (id % 4 == 3)
angle += 90;
processAngle();
setRadian_IN_RANGE();
angle = tempAngle;
}
void reshape(int w, int h)
{
glViewport(0, 0, (GLsizei)w, (GLsizei)h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(45.0, (GLfloat)w / (GLfloat)h, 0.01, 50.0);
glMatrixMode(GL_MODELVIEW);
}
void DrawSticksArroundYard(){
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, red);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, black);
GLUquadricObj *quadObj;
// Right-Line
glPushMatrix();
glTranslatef(6.8, 1.0 + fenceHeight, -7.0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.1, 0.1, 14.0, 10, 10);
glPopMatrix();
// Left-Line
glPushMatrix();
glTranslatef(-6.8, 1.0 + fenceHeight, -7.0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.1, 0.1, 14.0, 10, 10);
glPopMatrix();
// Back-Line
glPushMatrix();
glTranslatef(-6.8, 1.0 + fenceHeight, -7.0);
glRotatef(90, 0, 1, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.1, 0.1, 13.7, 10, 10);
glRotatef(-90, 0, 1, 0);
glPopMatrix();
// Front-Line
glPushMatrix();
glTranslatef(6.8, 1.0 + fenceHeight, 7.0);
glRotatef(-90, 0, 1, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.1, 0.1, 13.7, 10, 10);
glRotatef(90, 0, 1, 0);
glPopMatrix();
// Pin-Front-Right
glPushMatrix();
glTranslatef(6.8, 0, 7.0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Front-Left
glPushMatrix();
glTranslatef(-6.8, 0, 7.0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Back-Left
glPushMatrix();
glTranslatef(-6.8, 0, -7.0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Back-Right
glPushMatrix();
glTranslatef(6.8, 0, -7.0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Back-Center
glPushMatrix();
glTranslatef(0, 0, -7.0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Front-Center
glPushMatrix();
glTranslatef(0, 0, 7.0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Right-Center
glPushMatrix();
glTranslatef(6.8, 0, 0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
// Pin-Left-Center
glPushMatrix();
glTranslatef(-6.8, 0, 0);
glRotatef(-90, 1, 0, 0);
quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.1, 1.3 + fenceHeight, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
}
void DrawYardFloor(){
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, lightgreen);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, lightgreen);
glBegin(GL_POLYGON);
glNormal3f(0, 1, 0);
glVertex3f(-7.3, -0.005, -7.3);
glVertex3f(-7.3, -0.005, 7.3);
glVertex3f(7.3, -0.005, 7.3);
glVertex3f(7.3, -0.005, -7.3);
glEnd();
}
void DrawCenterPin(){
glRotatef(-90, 1, 0, 0);
GLUquadricObj *quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.2, 7, 10, 10);
glRotatef(90, 1, 0, 0);
}
void DrawBase(){
glRotatef(-90, 1, 0, 0);
GLUquadricObj *quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.5, 0.1, 2, 10, 10);
glRotatef(90, 1, 0, 0);
}
void DrawTop(){
glPushMatrix();
glTranslatef(0, 7, 0);
glRotatef(-90, 1, 0, 0);
GLUquadricObj *quadObj = gluNewQuadric();
gluCylinder(quadObj, 0.2, 0.0, 0.5, 10, 10);
glRotatef(90, 1, 0, 0);
glPopMatrix();
}
void DrawHorizontalStick(){
glLineWidth(15);
glColor3f(1.0, 0.0, 0.0);
glBegin(GL_LINES);
glVertex3f(0.0, 7.0, 0.0);
glVertex3f(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE), 0.0);
glEnd();
}
void DrawVerticalStick(){
glLineWidth(5);
glColor3f(1.0, 0.0, 0.0);
glBegin(GL_LINES);
glVertex3f(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE), 0.0);
glVertex3f(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE) - 1, 0.0);
glEnd();
}
void DrawCabin(){
// Back
glNormal3f(0.0, 0.0, -1.0);
glBegin(GL_POLYGON);
glVertex3f(0, 0, -1);
glVertex3f(0, 1, -1);
glVertex3f(2, 1, -1);
glVertex3f(2, 0, -1);
glEnd();
glNormal3f(0.0, 0.0, -1.0);
glBegin(GL_POLYGON);
glVertex3f(0, 1.7, -1);
glVertex3f(0, 2, -1);
glVertex3f(2, 2, -1);
glVertex3f(2, 1.7, -1);
glEnd();
glNormal3f(0.0, 0.0, -1.0);
glBegin(GL_POLYGON);
glVertex3f(0, 1, -1);
glVertex3f(0, 1.7, -1);
glVertex3f(0.2, 1.7, -1);
glVertex3f(0.2, 1, -1);
glEnd();
glNormal3f(0.0, 0.0, -1.0);
glBegin(GL_POLYGON);
glVertex3f(1.8, 1, -1);
glVertex3f(1.8, 1.7, -1);
glVertex3f(2, 1.7, -1);
glVertex3f(2, 1, -1);
glEnd();
// Front
glNormal3f(0.0, 0.0, 1.0);
glBegin(GL_POLYGON);
glVertex3f(2, 0, 1);
glVertex3f(2, 1, 1);
glVertex3f(0, 1, 1);
glVertex3f(0, 0, 1);
glEnd();
glNormal3f(0.0, 0.0, 1.0);
glBegin(GL_POLYGON);
glVertex3f(2, 1.7, 1);
glVertex3f(2, 2, 1);
glVertex3f(0, 2, 1);
glVertex3f(0, 1.7, 1);
glEnd();
glNormal3f(0.0, 0.0, 1.0);
glBegin(GL_POLYGON);
glVertex3f(0.2, 1, 1);
glVertex3f(0.2, 1.7, 1);
glVertex3f(0, 1.7, 1);
glVertex3f(0, 1, 1);
glEnd();
glNormal3f(0.0, 0.0, 1.0);
glBegin(GL_POLYGON);
glVertex3f(2, 1, 1);
glVertex3f(2, 1.7, 1);
glVertex3f(1.8, 1.7, 1);
glVertex3f(1.8, 1, 1);
glEnd();
// Floor
glNormal3f(0.0, -1.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(2, 0, -1);
glVertex3f(2, 0, 1);
glVertex3f(0, 0, 1);
glVertex3f(0, 0, -1);
glEnd();
// Top
glNormal3f(0.0, 1.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(2, 2, 1);
glVertex3f(2, 2, -1);
glVertex3f(0, 2, -1);
glVertex3f(0, 2, 1);
glEnd();
// Right
glNormal3f(1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(2, 0, -1);
glVertex3f(2, 1, -1);
glVertex3f(2, 1, 1);
glVertex3f(2, 0, 1);
glEnd();
glNormal3f(1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(2, 1.7, -1);
glVertex3f(2, 2, -1);
glVertex3f(2, 2, 1);
glVertex3f(2, 1.7, 1);
glEnd();
glNormal3f(1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(2, 1, -1);
glVertex3f(2, 1.7, -1);
glVertex3f(2, 1.7, -0.8);
glVertex3f(2, 1, -0.8);
glEnd();
glNormal3f(1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(2, 1, 0.8);
glVertex3f(2, 1.7, 0.8);
glVertex3f(2, 1.7, 1);
glVertex3f(2, 1, 1);
glEnd();
// Left
glNormal3f(-1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(0, 0, -1);
glVertex3f(0, 0, 1);
glVertex3f(0, 1, 1);
glVertex3f(0, 1, -1);
glEnd();
glNormal3f(-1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(0, 1.7, -1);
glVertex3f(0, 1.7, 1);
glVertex3f(0, 2, 1);
glVertex3f(0, 2, -1);
glEnd();
glNormal3f(-1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(0, 1, -1);
glVertex3f(0, 1, -0.8);
glVertex3f(0, 1.7, -0.8);
glVertex3f(0, 1.7, -1);
glEnd();
glNormal3f(-1.0, 0.0, 0.0);
glBegin(GL_POLYGON);
glVertex3f(0, 1, 0.8);
glVertex3f(0, 1, 1);
glVertex3f(0, 1.7, 1);
glVertex3f(0, 1.7, 0.8);
glEnd();
}
void darwCabin__FINAL(){
glPushMatrix();
glTranslatef(4.0 * cos(radian__IN_RANGE), 7.0 + 4.0 * sin(radian__IN_RANGE) - 3, 0.0);
glRotatef(angle, 0, 1, 0);
glPushMatrix();
glTranslatef(-1, 0, 0);
DrawCabin();
glPopMatrix();
glRotatef(-angle, 0, 1, 0);
glPopMatrix();
}
void display(void)
{
for (int i = 0; i < 2; i++) {
glutSetWindow(window[i]); // set the current window to window[i]
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64);
if (i == 1) {
gluLookAt(0.7, 0, 0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
glRotatef(-angle, 0, 1, 0);
glTranslatef(-4.0 * cos(radian__IN_RANGE), -5.4 + 4.0 * sin(radian__IN_RANGE), 0);
glRotatef(-angle, 0, 1, 0);
}
else if (i == 0) {
cpos[0] = zoom * cos(beta) * sin(alpha);
cpos[1] = zoom * sin(beta);
cpos[2] = zoom * cos(beta) * cos(alpha);
gluLookAt(cpos[0], cpos[1], cpos[2], 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
}
if (lightSource == true){
glLightfv(GL_LIGHT0, GL_POSITION, lpos);
glMaterialfv(GL_FRONT, GL_EMISSION, white);
glPushMatrix();
glTranslatef(lpos[0], lpos[1], lpos[2]);
glutSolidSphere(0.1, 10, 8);
glPopMatrix();
glMaterialfv(GL_FRONT, GL_EMISSION, black);
}
DrawYardFloor();
DrawSticksArroundYard();
DrawCenterPin();
DrawBase();
DrawTop();
glRotatef(angle, 0, 1, 0);
for (int j = 0; j < 4; j++){
glMaterialfv(GL_FRONT, GL_SPECULAR, white);
glMaterialf(GL_FRONT, GL_SHININESS, 64);
if (id % 4 == 0)
{
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, green);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, black);
}
else if (id % 4 == 1)
{
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, blue);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, black);
}
else if (id % 4 == 2)
{
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, white);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, black);
}
else if (id % 4 == 3)
{
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, cyan);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, black);
}
glPushMatrix();
glRotatef(j * 360 / 4, 0, 1, 0);
keepTrackOfID();
DrawHorizontalStick();
DrawVerticalStick();
darwCabin__FINAL();
id++;
glPopMatrix();
}
glRotatef(-angle, 0, 1, 0);
glFlush();
glutSwapBuffers();
}
}
void keyboard(unsigned char key, int x, int y)
{
static int polygonmode[2];
switch (key) {
case 27:
exit(0);
break;
case 'x':
if (lightSource == true)
lpos[0] = lpos[0] + 0.2;
glutPostRedisplay();
break;
case 'X':
if (lightSource == true)
lpos[0] = lpos[0] - 0.2;
glutPostRedisplay();
break;
case 'y':
if (lightSource == true)
lpos[1] = lpos[1] + 0.2;
glutPostRedisplay();
break;
case 'Y':
if (lightSource == true)
lpos[1] = lpos[1] - 0.2;
glutPostRedisplay();
break;
case 'z':
if (lightSource == true)
lpos[2] = lpos[2] + 0.2;
glutPostRedisplay();
break;
case 'Z':
if (lightSource == true)
lpos[2] = lpos[2] - 0.2;
glutPostRedisplay();
break;
case '+':
if (zoom != 1.5)zoom = zoom - 0.5;
glutPostRedisplay();
break;
case '-':
if (zoom != 30)zoom = zoom + 0.5;
glutPostRedisplay();
break;
case '0':
if (lightSource == true){
glDisable(GL_LIGHT0);
lightSource = false;
}
else{
glEnable(GL_LIGHT0);
lightSource = true;
}
glutPostRedisplay();
break;
case 'e':
if (fenceHeight < 2)
fenceHeight += 0.5;
glutPostRedisplay();
break;
case 'd':
if (fenceHeight > -0.5)
fenceHeight -= 0.5;
glutPostRedisplay();
break;
case 'w':
glGetIntegerv(GL_POLYGON_MODE, polygonmode);
if (polygonmode[0] == GL_FILL)
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);
else glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
glutPostRedisplay();
break;
case 'n':
angle++;
processAngle();
setRadian_IN_RANGE();
glutPostRedisplay();
break;
case 'm':
angle--;
processAngle();
setRadian_IN_RANGE();
glutPostRedisplay();
break;
default:
break;
}
}
void mouse(int button, int state, int x, int y)
{
switch (button) {
case GLUT_LEFT_BUTTON:
signal = 0;
if (speed <= 15)
speed++;
break;
case GLUT_MIDDLE_BUTTON:
case GLUT_RIGHT_BUTTON:
signal = 1;
if (speed >= 1)
speed--;
break;
default:
break;
}
}
void specialkey(GLint key, int x, int y)
{
switch (key) {
case GLUT_KEY_RIGHT:
alpha = alpha + PI / 180;
if (alpha > 2 * PI) alpha = alpha - 2 * PI;
glutPostRedisplay();
break;
case GLUT_KEY_LEFT:
alpha = alpha - PI / 180;
if (alpha < 0) alpha = alpha + 2 * PI;
glutPostRedisplay();
break;
case GLUT_KEY_UP:
if (beta < 0.45*PI) beta = beta + PI / 180;
glutPostRedisplay();
break;
case GLUT_KEY_DOWN:
if (beta > -0.05*PI) beta = beta - PI / 180;
glutPostRedisplay();
break;
default:
break;
}
}
void anim(){
if (signal == 0){
angle++;
glutPostRedisplay();
Sleep((int)(50 / speed));
}
else if (signal == 1){
if (speed != 0){
angle++;
glutPostRedisplay();
Sleep((int)(50 / speed));
}
}
}
int main(int argc, char** argv)
{
writemessage();
fillArray();
processAngle();
setRadian_IN_RANGE();
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
glutInitWindowSize(500, 500);
glutInitWindowPosition(0, 0);
window[0] = glutCreateWindow("First");
init();
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutIdleFunc(anim);
glutMouseFunc(mouse);
glutKeyboardFunc(keyboard);
glutSpecialFunc(specialkey);
glutInitWindowSize(500, 500);
glutInitWindowPosition(600, 10);
window[1] = glutCreateWindow("Second");
init();
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutIdleFunc(anim);
glutMouseFunc(mouse);
glutKeyboardFunc(keyboard);
glutSpecialFunc(specialkey);
glutMainLoop();
return 0;
}

Answer 1

Lighting for lines works just the same as for other objects. The color/brightness is calculated based on normals, and the lighting and material parameters.
If you're using immediate mode draw commands, you can specify normals with glNormal3f() before the glVertex3f() calls you make for the lines. If you don't specify the normal this way, whatever is the current normal based on earlier calls to glNormal*() will be used as the normal for your lines.
Now, the obvious follow-up question is: What is the normal of a line?
The simple answer is: Whatever you want it to be, to give you the desired result.
For a typical example, if you draw an analytic surface in wireframe mode, the normals of this analytic surface can be used as the normals. This will give a wireframe model where the shading/brightness corresponds to the shape of the surface.
In your example, the most obvious and arguably best approach is to not draw lines, but represent the geometry with polygons, using some kind of thin beam/cylinder. But as an exercise, we can figure out how this would work with lines anyway.
In this case, you want the line to represent an infinitely thin cylinder. An actual cylinder would have normals pointing outwards for each vertex. But since the line has only two vertices, you have to pick one single direction among the infinite set of vectors that point outwards from the end point, and are orthogonal to the line.
I believe you would get reasonable results by choosing the normal vector that is closest to pointing towards the viewpoint. This would result in the brightness you would get from looking at the center line of the cylinder if you actually used a cylinder. These normals could be calculated by:
Apply your model transformation to the original end points of the line, v1 and v2. Let's called the transformed end points v1t and v2t.
Calculate the direction vector of the transformed line as:
v1d = v2t - v1t
v1d.normalize()
Calculate the vector from line end point to view point vp, and orthogonalize it relative to the direction of the line, and normalize it:
v1n = vp - v1
v1n -= dot(v1d * v1n) * v1d
v1n.normalize()
Apply the inverse model transform to v1n to get the normal in the original object space.
Perform equivalent calculation for second vertex.
You could achieve the same result by doing the inverse transformation on the view point, and then calculating the normals directly in object space.