Rotation
A rotation is a geometric transformation that turns points or objects about a fixed center, origin, or axis through an angle while preserving distances and angles.
Geometry for Programmers
A rotation is a geometric transformation that turns points around a fixed center, axis, or origin while preserving distances and angles.
- How it is used
- Applies rotation as a common graphics and design transformation, then combines it with other geometric operations.
- How deep it goes
- Derives a 2D coordinate formula, reviews sine behavior, and develops homogeneous matrix composition through 3D extensions.
- Examples
- Uses rotated squares, a center-rotation composition, and a rectangle transformed by composed SymPy-style matrices.
- What you can do after
- Build it from scratch, apply 2D rotation formulas, and combine rotations with other transformations as one matrix.
CSS in Depth, Second Edition
A rotation is a geometric transformation that turns an object around a fixed point or axis.
- How it is used
- Uses rotation to change an element’s rendered orientation in static layouts, transitions, animations, and three-dimensional effects.
- How deep it goes
- Explains angle direction, units, axes, transform order, and document-flow consequences through a progressively modified card example.
- Examples
- Demonstrates rotated cards, negative angles, combined translation and rotation, and three-axis rotation diagrams.
- What you can do after
- Apply it via CSS transform functions, choose suitable angle units and axes, and diagnose unexpected movement caused by transform order.
Math for Web Design
A rotate transform is a CSS transformation operation that rotates an element around its transform origin.
- How it is used
- Applies geometric angles to CSS transforms, hover effects, cursor tracking, and rotary controls.
- How deep it goes
- Explains degrees, radians, centers, vectors, atan2, distance scaling, and angle normalization through frontend calculations.
- Examples
- Uses CSS rotate(), cursor-following arrows, grid-card hover tilt, and a volume knob with bounded angles.
- What you can do after
- Apply rotation via CSS and JavaScript, calculate target-facing angles, and build pointer-driven hover or dial interactions.
Deep Learning with PyTorch, Second Edition
A data augmentation transform that turns an image or volume around an axis, here constrained to the X-Y plane for CT data.
- How it is used
- Augments CT training candidates with controlled spatial variation while preserving their representative nature.
- How deep it goes
- Implements random 0–2π X-Y rotation with a 4×4 affine matrix, then resamples through PyTorch grid functions.
- Examples
- Uses a positive nodule sample and a runnable rotation branch that constructs a sine-cosine matrix.
- What you can do after
- Apply it via PyTorch affine_grid and grid_sample to rotate CT candidates during augmentation.
Read how Deep Learning with PyTorch, Second Edition explains rotation →
Related concepts
- sine functionuses · The sine function is a periodic trigonometric function that maps a real number or angle to a value between −1 and 1.
- cosine functionuses · The cosine function is a periodic trigonometric function that maps a real number or angle to a value between −1 and 1.
- compositionused by · Composition is a technique for combining simpler functions, components, or operations into a larger structure or behavior.
- color scaleconfigures · A color scale is a mapping from data values or categories to colors, often arranged as a continuous gradient or discrete set for visual representation.
- positional embeddingused by · A positional embedding is a learned or fixed representation that encodes an element’s position or order in a sequence and is incorporated into its content representation.
- radial visualizationused by · A radial visualization arranges graphical marks or data encodings around a center using angular and radial coordinates.
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