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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?

<p>For more accurate calculations (D)</p> Signup and view all the answers

Which mathematician is credited with the development of coordinate geometry?

<p>Descartes (B)</p> Signup and view all the answers

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

<p>Whether Y or Z should represent the vertical axis (B)</p> Signup and view all the answers

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

<p>A mathematical framework for geometry (D)</p> Signup and view all the answers

Which of the following describes Cartesian Coordinates?

<p>A system that uses height, width, and depth (C)</p> Signup and view all the answers

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

<p>To indicate the direction a face is pointing (C)</p> Signup and view all the answers

How does Lambertian reflectance describe light behavior?

<p>It describes light reflection independent of viewing angle (A)</p> Signup and view all the answers

What is the main strategy behind Gouraud shading?

<p>Using the average vertex normals to define shading (D)</p> Signup and view all the answers

What problem is commonly associated with Gouraud shading?

<p>Visible edges from interpolated vertex shades (B)</p> Signup and view all the answers

How does Phong shading differ from Gouraud shading?

<p>It interpolates face normals rather than vertex normals (B)</p> Signup and view all the answers

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

<p>The surface appears brighter (C)</p> Signup and view all the answers

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

<p>It makes rendering slower and more complex (C)</p> Signup and view all the answers

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

<p>Phong shading (C)</p> Signup and view all the answers

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

<p>They can be easily converted to 2D data. (D)</p> Signup and view all the answers

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

<p>World origin, vertices, and edges. (D)</p> Signup and view all the answers

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

<p>It simplifies the calculation of the normal vector. (C)</p> Signup and view all the answers

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

<p>Cross product of two edges of the triangle. (A)</p> Signup and view all the answers

What do perspective and orthographic projections have in common?

<p>Both convert 3D data to 2D space. (C)</p> Signup and view all the answers

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

<p>It determines the closest point at which objects are rendered. (C)</p> Signup and view all the answers

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

<p>Albrecht Dürer (B)</p> Signup and view all the answers

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

<p>Employing only quads for all animations. (D)</p> Signup and view all the answers

Flashcards

Polygon Mesh

A 3D object created by connecting points (vertices) with lines (edges), forming triangular faces.

Triangle

A 3D shape composed of three points (vertices) connected by lines (edges), forming a single flat surface.

3D Rendering

The process of converting 3D data into a 2D image that can be displayed on a screen.

Perspective Projection

A mathematical technique used in rendering to project 3D objects onto a 2D screen, simulating how we see in real life, with vanishing points.

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Orthographic Projection

A mathematical technique used in rendering to project 3D objects onto a 2D screen, without simulating depth or perspective.

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Normal Vector

A vector perpendicular to a surface, indicating its direction and orientation.

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Transformation

The ability to control the position, orientation, and size of a 3D object in virtual space.

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Clipping Planes

Used to describe the boundary of what the camera renders, excluding objects too close or too far.

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Cartesian Coordinates

A system used to define the position of points in 3D space using three coordinates: X (width), Y (height), and Z (depth).

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Longitude and Latitude

A system used to define the position of points on a flat surface using two coordinates: longitude (X) and latitude (Y).

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Analytic Geometry

The branch of mathematics that studies the properties of geometric figures using algebraic methods.

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3D Meshes

A system for representing 3D objects using a collection of points (vertices) connected by lines (edges) and surfaces (faces).

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3D Up Direction

The direction that is considered "up" in a 3D space, which can differ based on the software used.

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3D Visualization

The process of translating 3D information into a form that can be displayed on a computer screen.

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Solid Geometry

A system for representing 3D objects that consists of a series of points (vertices) connected by lines (edges) and surfaces (faces), which are stored as numerical data.

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Computer Graphics

The process of using mathematical formulas and algorithms to calculate and manipulate 3D objects and environments.

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Lambertian Reflectance

A method for calculating how bright a triangle should appear based on its angle relative to a light source. The smaller the angle between the normal vector and the light direction, the brighter the triangle appears.

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Normal Interpolation

A technique for smoothing out the appearance of 3D models by interpolating normals between vertices. It creates a more gradual transition between individual polygons, reducing the jagged, pixelated look.

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Gouraud Shading

One of the first methods for shading 3D models by calculating the average normal of its neighboring faces. It creates a smoother appearance than flat shading, but can still exhibit noticeable sharp edges.

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Phong Shading

A technique that interpolates the normals themselves, rather than just averaging them, resulting in a smoother and more realistic appearance compared to Gouraud shading.

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Edge Effect

The effect of sharp edges or visible polygons in a 3D model, often caused by low polygon count or flat shading techniques.

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Polycount

The number of polygons used to create a 3D model. A higher polycount generally results in a smoother and more detailed model.

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Vertex Normal

A technique that involves calculating the average normal of the neighboring faces and interpolating this information to create smooth gradients. It is a fundamental technique in 3D graphics, offering a significant visual improvement in rendering.

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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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