Grafika Komputer : Pertemuan 7 (Part 1) Transformasi 2D dengan Metode Konvensional

Summary

In this video on computer graphics, viewers are introduced to 2D transformations, including translation, scaling, and rotation. The presenter explains each transformation's definition, mathematical formulas, and practical examples, demonstrating how to manipulate points on a graph. Translation is described as shifting points, scaling as resizing objects, and rotation as turning points around an origin. Additionally, the video covers how to perform these transformations with respect to a non-origin point. This foundational knowledge sets the stage for more advanced topics in future lectures, making it essential for anyone interested in computer graphics.

Takeaways

• 😀 Transformation in computer graphics primarily involves manipulating the location of points or pixels.
• 🔄 There are three basic transformations: Translation, Scaling, and Rotation.
• ➡️ Translation shifts a point (x, y) by adding specified translation values (TX, TY) to its coordinates.
• 🔢 The formula for translation is (x', y') = (x + TX, y + TY).
• 📏 Scaling enlarges or reduces an object based on scaling factors (SX, SY) for the x and y directions.
• 🧮 The formula for scaling is (x', y') = (x * SX, y * SY).
• 🔄 Rotation involves rotating points around the origin (0,0) using trigonometric functions for the angle θ.
• ⚙️ The formulas for rotation are x' = x * cos(θ) - y * sin(θ) and y' = x * sin(θ) + y * cos(θ).
• 🔍 For arbitrary points, transformations involve translating the point to the origin, applying the transformation, and then translating back.
• 📽️ The video sets the stage for future discussions on using matrices in transformation processes.

Q & A

What is the definition of transformation in computer graphics?

Transformation is a method used to manipulate the location of points, specifically the pixels in an image.

What are the three primary types of 2D transformations discussed in the video?

The three primary types of 2D transformations are translation (shifting), scaling (resizing), and rotation.

How is translation defined in the context of 2D transformations?

Translation is defined as moving a point a certain distance along the x-axis and y-axis, represented by adding values to the original coordinates.

Can you provide the formula used for translation?

The general formula for translation is expressed as: (x', y') = (x + tx, y + ty), where (tx, ty) are the translation distances.

What is scaling in the context of transformations?

Scaling is the process of resizing an object by a scale factor in the x and y directions, which involves multiplying the original coordinates by specific scale factors.

What operation is used in scaling transformations?

Scaling transformations involve multiplication of the coordinates by the scale factors.

How is rotation defined for 2D transformations?

Rotation involves turning a point around a specific center point, typically the origin (0,0), by a specified angle.

What are the formulas for calculating the new coordinates after rotation?

The formulas for rotation are: x' = x * cos(θ) - y * sin(θ) and y' = x * sin(θ) + y * cos(θ), where θ is the angle of rotation.

How do transformations work with arbitrary points rather than the origin?

For arbitrary points, the transformation involves first translating the point to the origin, performing the desired transformation, and then translating it back to its original position.

What is the significance of using matrices in transformations?

Matrices provide a systematic way to perform multiple transformations through matrix multiplication, allowing for efficient computation and combination of transformations.