| import streamlit as st | |
| import pandas as pd | |
| st.subheader(":red[**Transformation**]") | |
| st.write("**What is Transformation?**") | |
| st.write(""" | |
| a transformation refers to the operation of changing the position, size, orientation, or shape of a geometric object while maintaining some of its properties. Common types of transformations include: | |
| - Translation (shifting an object). | |
| - Rotation (turning an object). | |
| - Scaling (resizing an object). | |
| - Reflection (flipping an object across a line). | |
| - Shearing (slanting an object). | |
| """) | |
| st.write("**What is an Affine Transformation?**") | |
| st.write(""" | |
| An affine transformation is a specific type of transformation that preserves: | |
| - Points. | |
| - Straight lines. | |
| - Parallelism (parallel lines remain parallel after the transformation). | |
| Affine transformations can include: | |
| - Translation. | |
| - Rotation. | |
| - Scaling. | |
| -Shearing. | |
| Affine transformations do not necessarily preserve angles or lengths, but they do maintain the general shape and relative proportions of geometric figures. | |
| """) | |
| st.write("**Mathematical Representation of Affine Transformations**") | |
| st.write("Affine transformations can be expressed using matrix multiplication and vector addition:") | |
| code=""" | |
| y=A⋅x+b | |
| """ | |
| st.code(code,language="python") | |
| st.write(""" | |
| Where: | |
| x: Input vector (original point coordinates). | |
| y: Output vector (transformed point coordinates). | |
| A: Transformation matrix (2x2 for 2D transformations). | |
| b: Translation vector. | |
| """) | |