Project 1a — Computer Graphics

Purpose

Learn how to use affine transformations to position objects in 3-space.

Resources

OpenGL Transformations and Matrices — moving, scaling, and rotating objects.
OpenGL Shading — lighting the scene.
GLFW Input Handling — adding keyboard inputs.
GLM — convenient OpenGL mathematics library.
GLSL Data Types — useful for shader programming.

Set Up

Use one of: OpenGL or WebGL.
For OpenGL, use the supplied code base.
For WebGL, starter code is not provided.

Task 1: Grid (5 points)

Perspective view of an integer grid on the horizontal Y equals zero plane. The grid is centered at the origin, with the positive X axis shown in red, the positive Y axis shown vertically in green, and the positive Z axis shown in blue. — Example view of the 3D grid and coordinate axes.

Draw an integer grid on the Y = 0 plane for the rectangle from (-5, 0, -5) to (+5, 0, +5).

Draw the positive portion of each axis, with length 5:

X axis: red
Y axis: green
Z axis: blue

Task 2: Camera Rotations (5 points)

Camera-orbit illustration: the blue circle is parallel to the equator; the red circle is orthogonal to it.

Use perspective projection.
Place the camera so that you can see the whole scene. Use glm::LookAt to generate the View matrix.
Press C to select the camera. (This sets the context of subsequent ← and → commands)
Use ↑ and ↓ to rotate the camera along the red circle orthogonal to the equator.
Choose the up direction so the camera always points to the origin. Test this by moving the camera across the north pole.

Camera viewing direction toward the origin and an up direction.

Task 3: Draw the Robot Arm (25 points)

Photograph of a three-joint robotic arm with curved arrows indicating rotations J1, J2, and J3 at the base, first arm joint, and second arm joint. — Reference illustration shows rotational joints J2 and J3 implemented in Project 1B.

Three-dimensional robot-arm model in a Blender viewport. A large polygonal base supports a rectangular first arm, a polygonal joint, and a cylindrical second arm. — Example 3D robot-arm model.

The robot arm consists of the following parts:

Base: truncated tetrahedron placed on the X–Z plane.
Arm 1: rectangular box emanating from and hinged at the center of the base.
Joint: dodecahedron of appropriate radius at the other end of Arm 1.
Arm 2: cylinder connected to the center of the joint.
Before assembling in the code, place the parts onto the grid, and show them shifted to not overlap.

Geometry and models

Create triangulated objects in .obj format, for example by using Blender.
Hint: For later use, load the models so that their model coordinate origin is the pivot (rotation center) point.
Translate and rotate the models within your project to their world coordinates.
Load or generate correct normals for later use.

To load .obj files, you can use your own loader OR tinyobjloader OR adjust the supplied OBJ loader:

bool loadOBJ(
    const char *path,
    std::vector<...>& out_vertices,
    std::vector<...>& out_uvs,
    std::vector<...>& out_normals,
    std::vector<...>& out_indices
)

Hint: You may want to familiarize yourself with obj reader errors

What to Submit

Your modified source files — CPP, shader, HTML, OBJ, as appropriate. File paths used to load models must be relative to the source directory; do not use absolute paths specific to your computer.
A link to a screen capture of your running program showcasing the implementation of all tasks, using Recordit or a similar screen-recording tool. List the tasks in order and demonstrate each task, or state that you did not implement it and briefly explain why.