Affinely

In a manner characterized by an affine transformation. Affine transformations, in mathematics, are linear transformations followed by a translation. They preserve collinearity (points on a line remain on a line) and ratios of distances, but not necessarily angles or lengths. The term "affinely" is used to describe a relationship or process that adheres to the principles of affine geometry, meaning it can be described using these transformations. This includes concepts like scaling, shearing, and reflecting a figure but crucially also translation of the figure's coordinate system or position within the affine plane.

Affinely meaning with examples

• The image was warped affinely to correct for perspective distortion, allowing the objects to be viewed from a consistent perspective even with significant camera angle. This processing step ensures precise measurement and analysis can be performed based on these re-aligned parameters.
• The computer graphics software transforms 3D objects affinely when they are moved or rotated, preserving their overall shape and internal structure while changing their position and orientation within the virtual space. This maintains the spatial integrity of the scene.
• During image registration, two images are aligned affinely to match corresponding features. This process often uses image matching algorithms such as normalized cross-correlation to determine the best parameters for alignment.
• The researcher manipulated data affinely to remove the effects of systematic errors. Using the resulting data, the researchers could then draw accurate conclusions about the underlying phenomena by eliminating bias.
• The geometric shapes were arranged affinely in the design, so all elements were consistent in their proportions, allowing the viewer to clearly understand the relationships between them no matter their absolute location.