Kelas Grafika Komputer | Transformasi 2D (Metode konvensional)

Summary

This video explains two-dimensional transformations in computer graphics, focusing on conventional methods: translation, scaling (schelling), and rotation. It covers how each transformation manipulates the position of points in a 2D space using mathematical operations like addition and multiplication. The video provides step-by-step examples and formulas for applying these methods, demonstrating how to shift, scale, and rotate points. The session introduces basic concepts with practical illustrations and emphasizes understanding the process of transformation for geometric shapes, preparing viewers for more advanced topics in future lessons.

Takeaways

• 😀 Two-dimensional transformations manipulate the position of a point on a screen or display.
• 😀 The conventional methods of 2D transformation include translation, scaling (schelling), and rotation.
• 😀 Translation involves shifting an object along a straight line without changing its shape or size, using an addition operation.
• 😀 The translation formula involves adding shift values (trx and try) to the original coordinates (x, y) to get the new location.
• 😀 Scaling (schelling) changes the size of an object by multiplying its coordinates with scaling factors (sx and sy) along the x and y axes.
• 😀 The scaling method uses multiplication of the original coordinates with scaling factors to achieve resizing.
• 😀 Rotation involves rotating an object around a point, typically the origin (0,0), using trigonometric functions (cosine and sine).
• 😀 Rotation is calculated using the radius (r) and the angle (theta) to find the new position of points after rotation.
• 😀 For rotation around an arbitrary point, a three-step process is followed: translation to origin, rotation, and then translation back to the original position.
• 😀 The lecturer also mentions matrix methods for 2D transformations, which will be covered in future lessons, as a more advanced approach.

Q & A

What is the main topic of this video script?

The main topic of the video script is two-dimensional transformations, focusing on methods like translation, scaling, and rotation, as well as the differences between the conventional and matrix methods.

What are the two methods used in two-dimensional transformation?

The two methods used in two-dimensional transformation are the conventional method and the matrix method.

What is the purpose of transformation in computer graphics?

Transformation in computer graphics is used to manipulate the location of a point, which refers to changing the position of a pixel in an image or on a display screen.

What mathematical operation is used in the translation method?

The translation method uses the addition operation, where the position of a point is shifted along the x-axis and y-axis by specific amounts.

Can you explain how the translation method works with an example?

In the translation method, a point is shifted by specified values along the x and y axes. For example, if a point A has coordinates (2, 4) and is shifted by (4, 2), the new coordinates would be (6, 6), as we add the shift values to the original coordinates.

How does the scaling (schelling) method differ from the translation method?

The scaling (schelling) method uses multiplication rather than addition. In this method, the coordinates of a point are multiplied by scaling factors for the x-axis and y-axis, which changes the size of the object while keeping the shape consistent.

What is the formula for the scaling (schelling) method?

The formula for the scaling method is (x', y') = (x * Sx, y * Sy), where (x, y) are the original coordinates, and Sx and Sy are the scaling factors for the x and y axes respectively.

What is the purpose of the rotation method in two-dimensional transformation?

The rotation method is used to rotate a point or object around a specified center point by a given angle, changing its orientation while maintaining its shape and size.

How is the rotation method applied when the center of rotation is at the origin (0, 0)?

When the center of rotation is at the origin (0, 0), the rotation of a point is calculated using the trigonometric formulas x' = r * cos(θ) and y' = r * sin(θ), where r is the distance from the origin to the point and θ is the rotation angle.

What steps are involved in performing a rotation around an arbitrary center point?

To rotate around an arbitrary center point, three steps are involved: 1) Translate the point so the center of rotation becomes the origin, 2) Apply the rotation, 3) Translate the point back to its original position using the center of rotation.