Below is example Java OpenGL coding:

import com.jogamp.common.nio.Buffers; import com.jogamp.opengl.GL4; import com.jogamp.opengl.GLAutoDrawable; import com.jogamp.opengl.GLContext; import com.jogamp.opengl.GLEventListener; import com.jogamp.opengl.awt.GLCanvas; import org.joml.Matrix4f;

import javax.swing.*; import java.nio.FloatBuffer;

import static com.jogamp.opengl.GL4.*;

public class Program4_3 extends JFrame implements GLEventListener { private GLCanvas myCanvas; private int renderingProgram; private int vao[] = new int[1]; private int vbo[] = new int[2]; private float cameraX, cameraY, cameraZ; private float cubeLocX, cubeLocY, cubeLocZ; private float pyrLocX, pyrLocY, pyrLocZ;

private FloatBuffer vals = Buffers.newDirectFloatBuffer(16); // utility buffer for transferring matrices private Matrix4f pMat = new Matrix4f(); // perspective matrix private Matrix4f vMat = new Matrix4f(); // view matrix private Matrix4f mMat = new Matrix4f(); // model matrix private Matrix4f mvMat = new Matrix4f(); // model-view matrix private int pLoc, mvLoc; private float aspect; private double elapsedTime, startTime, tf;

public Program4_3() { setTitle("Chapter4 - program3"); setSize(600, 600); setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

myCanvas = new GLCanvas(); myCanvas.addGLEventListener(this); this.add(myCanvas);

/*Animator anmtr = new Animator(myCanvas); anmtr.start();*/

this.setVisible(true); }

public void init(GLAutoDrawable drawable) { GL4 gl = (GL4) GLContext.getCurrentGL(); renderingProgram = UtilsV7.createShaderProgram("./shaders/vertShader4_1_2.glsl", "./shaders/fragShader4_2.glsl"); setupVertices(); cameraX = 0.0f; cameraY = 0.0f; cameraZ = 8.0f; cubeLocX = 0.0f; cubeLocY = -2.0f; // shifted down the Y-axis to reveal perspective cubeLocZ = 0.0f; pyrLocX = 2.0f; // shifted right pyrLocY = 2.0f; // shifted down the Y-axis to reveal perspective pyrLocZ = 0.0f;

}

public void reshape(GLAutoDrawable drawable, int x, int y, int width, int height) { }

public void dispose(GLAutoDrawable drawable) { }

public void display(GLAutoDrawable drawable) { GL4 gl = (GL4) GLContext.getCurrentGL(); gl.glClear(GL_DEPTH_BUFFER_BIT); gl.glClear(GL_COLOR_BUFFER_BIT); gl.glUseProgram(renderingProgram);

// get references to the uniform variables for the MV and projection matrices pLoc = gl.glGetUniformLocation(renderingProgram, "p_matrix"); mvLoc = gl.glGetUniformLocation(renderingProgram, "mv_matrix");

aspect = (float) myCanvas.getWidth() / (float) myCanvas.getHeight(); pMat.setPerspective((float) Math.toRadians(60.0f), aspect, 0.1f, 1000.0f);

// build view matrix vMat.translation(-cameraX, -cameraY, -cameraZ);

// draw the cube (use buffer #0) mMat.translation(cubeLocX, cubeLocY, cubeLocZ); mvMat.identity(); mvMat.mul(vMat); mvMat.mul(mMat); // copy matrices and variables to corresponding uniform variables // by giving the uniform variable ID, one matrix to be sent, not transposed, and a pointer to the value sent gl.glUniformMatrix4fv(mvLoc, 1, false, mvMat.get(vals)); gl.glUniformMatrix4fv(pLoc, 1, false, pMat.get(vals)); // associate VBO with the corresponding vertex attribute in the vertex shader gl.glBindBuffer(GL_ARRAY_BUFFER, vbo[0]); // Sending to the location ID, 3 vertices of type float, not normalized, and with 0 offsets gl.glVertexAttribPointer(0, 3, GL_FLOAT, false, 0, 0); gl.glEnableVertexAttribArray(0); // adjust OpenGL settings and draw model gl.glEnable(GL_DEPTH_TEST); gl.glDepthFunc(GL_LEQUAL); gl.glDrawArrays(GL_TRIANGLES, 0, 36);

mMat.translation(pyrLocX, pyrLocY, pyrLocZ); mvMat.identity(); mvMat.mul(vMat); mvMat.mul(mMat); gl.glUniformMatrix4fv(mvLoc, 1, false, mvMat.get(vals)); gl.glUniformMatrix4fv(pLoc, 1, false, pMat.get(vals));

gl.glBindBuffer(GL_ARRAY_BUFFER, vbo[1]); gl.glVertexAttribPointer(0, 3, GL_FLOAT, false, 0, 0); gl.glEnableVertexAttribArray(0); gl.glEnable(GL_DEPTH_TEST); gl.glDepthFunc(GL_LEQUAL); gl.glDrawArrays(GL_TRIANGLES, 0, 18); }

private void setupVertices() { GL4 gl = (GL4) GLContext.getCurrentGL();

float[] cubePositions = {-1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -1.0f, -1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, -1.0f};

float[ ] pyramidPositions = { -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 0.0f, 1.0f, 0.0f, // front face 1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, 0.0f, 1.0f, 0.0f, // right face 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 0.0f, 1.0f, 0.0f, // back face -1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, 0.0f, 1.0f, 0.0f, // left face -1.0f, -1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, // base left front 1.0f, -1.0f, 1.0f, -1.0f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f // base right back }; gl.glGenVertexArrays(vao.length, vao, 0); gl.glBindVertexArray(vao[0]); gl.glGenBuffers(vbo.length, vbo, 0);

gl.glBindBuffer(GL_ARRAY_BUFFER, vbo[0]); FloatBuffer cubeBuf = Buffers.newDirectFloatBuffer(cubePositions);

gl.glBufferData(GL_ARRAY_BUFFER, cubeBuf.limit() * 4, cubeBuf, GL_STATIC_DRAW);

gl.glBindBuffer(GL_ARRAY_BUFFER, vbo[1]); FloatBuffer pyrBuf = Buffers.newDirectFloatBuffer(pyramidPositions);

gl.glBufferData(GL_ARRAY_BUFFER, pyrBuf.limit() * 4, pyrBuf, GL_STATIC_DRAW); } }

Shader Coding:

fragShader.glsl

#version 430 in vec4 varyingColor; out vec4 color; uniform mat4 mv_matrix; uniform mat4 p_matrix; void main(void) { color = varyingColor; } vertShader.glsl

#version 430 layout (location=0) in vec3 position; uniform mat4 mv_matrix; uniform mat4 p_matrix; out vec4 varyingColor;

void main(void) { gl_Position = p_matrix * mv_matrix * vec4(position,1.0); varyingColor = vec4(position,1.0) * 0.5 + vec4(0.5, 0.5, 0.5, 0.5); }

Questions :

1. How to modify above Java OpenGL coding to add sphere 3D shape. Be sure to properly specify the number of vertices in the glDrawArrays() command ? answer with coding (plug & play)

2. How to modify above OpenGL coding from answer No.1, so that the additional 3D shape rotates on its axis (just like the earths rotation, but we may choose which axis to rotate on, x, y, or z-axis) ? answer with coding (plug & play)