Computer Graphics and NumPy Essentials

Vocabulary flashcards covering NumPy basics, 3D graphics math, and course logistics mentioned in the lecture notes.

NumPy

Open-source Python library for numerical computing; provides the ndarray object and vectorized operations for array-based math.

ndarray

NumPy’s core multi-dimensional array data structure used for numerical computations.

Array vs List

List is a Python built-in dynamic container (can hold mixed types); ndarray is homogeneous, fixed-size, and optimized for numeric computation.

shape

The dimensions of an array, given as a tuple (e.g., (3, 4) for 3 rows by 4 columns).

size

Total number of elements in an array (the product of its shape dimensions).

ndim

The number of axes (dimensions) of an array.

dtype

Data type of the elements in an array (e.g., int64, float64, str).

np.zeros

Creates an array filled with zeros with a specified shape.

np.ones

Creates an array filled with ones with a specified shape.

np.empty

Creates an uninitialized array; contents are whatever memory previously held.

reshape

Change the shape of an array without changing its data.

flatten

Return a copy of the array collapsed into one dimension.

linspace

Generate a specified number of evenly spaced values between start and stop (inclusive).

arange

Create values in a range with a fixed step; similar to Python range but returns an array.

Broadcasting

NumPy rule that automatically expands arrays to compatible shapes for elementwise operations.

dot product

Matrix product of two arrays; use A.dot(B) or A @ B to perform it.

element-wise multiplication

Multiplying corresponding elements of two arrays (A * B) rather than matrix multiplication.

Broadcasting example

A scenario where shapes like (2,4) and (2,1) broadcast to a common shape before the operation.

np.dot

NumPy function that performs the dot product (matrix multiplication) for arrays.

MOSS

Plagiarism-detection tool that compares code submissions for similarity.

GeoGebra

Online visualization tool for geometry, algebra, and calculus used to visualize planes, lines, and intersections.

Parametric equation

Describes lines or curves using a parameter t: x = x0 + a t, y = y0 + b t, z = z0 + c t in 3D.

Plane equation

Ax + By + Cz + D = 0; a plane in 3D with normal vector (A, B, C).

Normal vector

A vector perpendicular to a plane; coefficients (A, B, C) in the plane equation.

Distance from origin to plane

For Ax + By + Cz + D = 0, distance from origin is |D| / sqrt(A^2 + B^2 + C^2).

Right-handed coordinate system

3D orientation where X × Y points to +Z; common convention in graphics.

Parametric line in 3D

A line described by x = x0 + a t, y = y0 + b t, z = z0 + c t using a parameter t.

Rotation matrix

A 3×3 matrix that rotates a vector around a principal axis by angle θ.

RotX matrix

Rotation about the X-axis: [[1,0,0],[0,cosθ,-sinθ],[0,sinθ,cosθ]].

RotY matrix

Rotation about the Y-axis: [[cosθ,0,sinθ],[0,1,0],[-sinθ,0,cosθ]].

RotZ matrix

Rotation about the Z-axis: [[cosθ,-sinθ,0],[sinθ,cosθ,0],[0,0,1]].

Translation

Moving points by adding a translation vector (dx, dy, dz) to coordinates.

Scaling

Resizing by multiplying coordinates with scale factors (sx, sy, sz); can be uniform or nonuniform.

Mirroring

Reflection achieved by negative scaling along an axis (e.g., scale by -1 on an axis).

3D graphics pipeline

Sequence of operations to render 3D scenes: modeling (translate/rotate/scale), projection to 2D, and display.

Coordinate handedness

Right-handed vs left-handed systems; orientation affects rotation signs and axis directions.

Projection to 2D

Mapping 3D points to 2D screen coordinates (perspective or orthographic projection).

Geogebra visualization

Online tool to visualize planes, lines, and intersections in 2D/3D.

Plane normal vector vs plane constants

Normal vector (A,B,C) and distance term D define plane orientation and position.

3D vs 2D vectors

Vectors describe direction and magnitude in space; translation affects points, not the vector itself.

Linear space vs dimension

Linear space refers to evenly spaced samples (linspace); dimension is the number of axes in an array.

Python in graphics class

Used for programming assignments; not a math course but a tool for graphics work.

GDB/VS Code/PyCharm

Development environments favored for writing and debugging Python code.

Geometric transformation

Any operation that changes position, orientation, or size: translation, rotation, scaling, projection.

3D to 2D display

Objects exist in 3D; to display they are transformed (rotated/translated/scaled) and projected to 2D.

Broadcasting pitfalls

Relying on broadcasting when a strict matrix operation is intended can hide bugs and produce unintended results.