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Questions and Answers

Who laid the foundations of solid geometry that are still used today?

Ptolemy

Descartes

Gauss

Euclid (correct)

What coordinates are typically used to define a point in 3D space?

X, Y, Z (correct)

X, Y, W

X, Y, P

Y, Z, A

What does the third coordinate, Z, represent in world coordinates?

Volume

Width

Height

Depth (correct)

Why was it important for sailors and cartographers to develop a numerical coordinate system?

For more accurate calculations Signup and view all the answers

Which mathematician is credited with the development of coordinate geometry?

Descartes Signup and view all the answers

What disagreement exists regarding the definition of the vertical axis in 3D space across different software?

Whether Y or Z should represent the vertical axis Signup and view all the answers

What does the term 'Euclidean Space' refer to in the context of coordinates?

A mathematical framework for geometry Signup and view all the answers

Which of the following describes Cartesian Coordinates?

A system that uses height, width, and depth Signup and view all the answers

What is the primary purpose of a normal vector in 3D geometry?

To indicate the direction a face is pointing Signup and view all the answers

How does Lambertian reflectance describe light behavior?

It describes light reflection independent of viewing angle Signup and view all the answers

What is the main strategy behind Gouraud shading?

Using the average vertex normals to define shading Signup and view all the answers

What problem is commonly associated with Gouraud shading?

Visible edges from interpolated vertex shades Signup and view all the answers

How does Phong shading differ from Gouraud shading?

It interpolates face normals rather than vertex normals Signup and view all the answers

What happens when the angle between the light direction and the normal is small?

The surface appears brighter Signup and view all the answers

Why might increasing the polycount not always be the best solution for smoother geometry?

It makes rendering slower and more complex Signup and view all the answers

What technique evolved to refine the lighting calculations in 3D rendering?

Phong shading Signup and view all the answers

What is the primary reason triangles are used in 3D rendering?

They can be easily converted to 2D data. Signup and view all the answers

What are the three components necessary to render a triangle on screen?

World origin, vertices, and edges. Signup and view all the answers

Why is it important that a triangle is a planar shape in 3D rendering?

It simplifies the calculation of the normal vector. Signup and view all the answers

What mathematical concept is used to find the normal vector of a triangle?

Cross product of two edges of the triangle. Signup and view all the answers

What do perspective and orthographic projections have in common?

Both convert 3D data to 2D space. Signup and view all the answers

What does the near clip plane accomplish in 3D rendering?

It determines the closest point at which objects are rendered. Signup and view all the answers

Which historical figure conducted early experiments on 3D to 2D projection?

Albrecht Dürer Signup and view all the answers

What is a common workflow practice in 3D modeling concerning the types of meshes used?

Employing only quads for all animations. Signup and view all the answers

Study Notes

3D Pipeline History

Euclid (300 BCE) laid the foundation for solid geometry, which is still used today.
Mathematicians built upon this foundation, meaning the mathematical framework for 3D computer graphics was already in place when computer graphics emerged.
The key challenge became visualizing this 3D information on a computer screen.

Coordinates

Descartes introduced coordinate geometry, a system to define points in 3D space using coordinates.
Three coordinates (x, y, and z) are needed to specify a unique point in 3D space.
Coordinate systems were developed to map locations on the Earth(latitude and longitude) and generalized to any plane.

Visualization

3D information needs to be stored before being visualized.
The foundations for rendering 3D objects using triangles are explained.
Computer renders a 2D projection of 3D data.

Triangle-Based Rendering

Triangles are fundamental elements in 3D graphics.
Triangles define shapes in 3D space, which are stored and rendered on a screen as 2D shapes.
The calculation of triangles to be displayed on a screen uses math.

Projection Techniques

Perspective projection mimics how the human eye sees objects in real life: objects further away appear smaller.
Orthographic projection shows objects from a fixed viewpoint.

Shading Techniques

Lambertian reflectance models light reflecting off a surface, independent of the viewer.
Gouraud shading blends the normal vectors of the vertices of a triangle to shade the entire polygon.
Phong shading interpolates the normal vectors of a polygon on a per-pixel basis, yielding smoother shading transitions.

Normal Direction

Normal vectors are perpendicular to surfaces and used in shading calculations, allowing for a realistic look, including smooth shading.
The orientation/direction of the normal is critical to rendering calculations, as incorrect direction can lead to rendering errors.
The use of normal vectors is important for smooth and correct rendering.

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