Spatial Point Rotation Around Center Using Three Sequential Transformations

Rotating a spatial point P around a center point C can be implemented through three sequential coordinate transformations: The first transformation translates point C to the coordinate system origin, the second transformation rotates point P around the origin, and the third transformation translates point C back to its original position relative to the coordinate origin. When original image points are multiplied by transformation matrices, the resulting new image positions may not be integer values, requiring gray value interpolation to determine pixel intensities. Without changing the output image size, MATLAB's native imrotate function handles out-of-bound areas by setting their gray values to zero. This paper introduces an alternative control method imrotate_my that uses modulo operations for boundary handling, effectively displaying boundary changes during image rotation.

Additionally, different rotation effects can be achieved by adjusting transformation matrix parameters. For example, modifying rotation angle, direction, or speed can produce various image transformation effects. Alternative interpolation methods like bilinear interpolation or bicubic interpolation can also be employed to estimate gray values for out-of-range pixels more accurately, thereby improving boundary effects in rotated images. These advanced interpolation techniques provide better intensity estimation for pixels falling outside the original image boundaries.

In conclusion, by carefully selecting transformation matrices and interpolation methods, we can achieve superior image rotation results with enhanced visualization of rotation boundary changes. The implementation involves constructing appropriate affine transformation matrices and selecting optimal interpolation algorithms based on specific application requirements.