Please watch the following video of the translation used in freeCAD...
Translation is a fundamental transformation in computer graphics that moves an object from one position to another in a 2D or 3D space. Unlike other transformations such as scaling or rotation, translation preserves the shape and orientation of the object, altering only its position.
Key Concepts
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Definition: Translation involves shifting all points of an object by the same distance in a specified direction.
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Translation Vector: A translation is defined by a vector , where:
- : Translation along the x-axis.
- : Translation along the y-axis.
- : Translation along the z-axis (for 3D graphics).
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Transformation Matrix: Translation is represented using a homogeneous coordinate matrix to allow for consistent matrix multiplication.
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For 2D translation:
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For 3D translation:
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Point Translation: A point (in 2D) or (in 3D) is translated by multiplying its homogeneous coordinate vector with the translation matrix:
- Where is the original point, is the translated point, and is the translation matrix.
Example
2D Translation:
Suppose a point is translated by :
The new point is .
Applications
- Moving objects: Shifting the position of objects in animations, games, or simulations.
- Camera movement: Adjusting the viewpoint in a scene.
- Path planning: Moving objects along a trajectory.
Translation in 3D Graphics
For 3D, the process is similar but includes the z-dimension. A cube or other 3D model can be moved in any direction by applying a 3D translation matrix.
Translation is a cornerstone of computer graphics, forming the basis for more complex transformations like scaling, rotation, and perspective transformations. It plays a critical role in rendering, animation, and interactive graphics!
Here's the Python script for experimenting with translation using freeCAD.
import FreeCAD
import FreeCADGui
from PySide2 import QtWidgets
class TranslationApp(QtWidgets.QWidget):
def __init__(self):
super().__init__()
self.setWindowTitle("3D Translation in FreeCAD")
self.setGeometry(300, 300, 300, 200)
# UI Components
layout = QtWidgets.QVBoxLayout()
# Create a cube button
self.create_cube_btn = QtWidgets.QPushButton("Create Cube")
self.create_cube_btn.clicked.connect(self.create_cube)
layout.addWidget(self.create_cube_btn)
# Translation input fields
self.tx_input = QtWidgets.QLineEdit()
self.tx_input.setPlaceholderText("Translation X")
layout.addWidget(self.tx_input)
self.ty_input = QtWidgets.QLineEdit()
self.ty_input.setPlaceholderText("Translation Y")
layout.addWidget(self.ty_input)
self.tz_input = QtWidgets.QLineEdit()
self.tz_input.setPlaceholderText("Translation Z")
layout.addWidget(self.tz_input)
# Apply translation button
self.apply_translation_btn = QtWidgets.QPushButton("Apply Translation")
self.apply_translation_btn.clicked.connect(self.apply_translation)
layout.addWidget(self.apply_translation_btn)
# Reset button
self.reset_btn = QtWidgets.QPushButton("Reset Cube Position")
self.reset_btn.clicked.connect(self.reset_position)
layout.addWidget(self.reset_btn)
self.setLayout(layout)
self.obj = None # Store the created object
def create_cube(self):
"""Creates a cube in FreeCAD."""
if not FreeCAD.ActiveDocument:
FreeCAD.newDocument("TranslationDemo")
else:
FreeCAD.ActiveDocument.clearAllObjects()
self.obj = FreeCAD.ActiveDocument.addObject("Part::Box", "Cube")
self.obj.Length = 10
self.obj.Width = 10
self.obj.Height = 10
FreeCAD.ActiveDocument.recompute()
FreeCADGui.ActiveDocument.ActiveView.setAnimationEnabled(True)
QtWidgets.QMessageBox.information(self, "Cube Created", "A cube has been created.")
def apply_translation(self):
"""Applies translation to the cube."""
if self.obj is None:
QtWidgets.QMessageBox.warning(self, "Error", "Create a cube first!")
return
try:
tx = float(self.tx_input.text())
ty = float(self.ty_input.text())
tz = float(self.tz_input.text())
# Apply translation
translation_vector = FreeCAD.Vector(tx, ty, tz)
self.obj.Placement.Base += translation_vector
FreeCAD.ActiveDocument.recompute()
QtWidgets.QMessageBox.information(self, "Success", f"Translated by ({tx}, {ty}, {tz})")
except ValueError:
QtWidgets.QMessageBox.warning(self, "Invalid Input", "Please enter valid numbers for translation.")
def reset_position(self):
"""Resets the cube's position to the origin."""
if self.obj is None:
QtWidgets.QMessageBox.warning(self, "Error", "Create a cube first!")
return
self.obj.Placement.Base = FreeCAD.Vector(0, 0, 0)
FreeCAD.ActiveDocument.recompute()
QtWidgets.QMessageBox.information(self, "Position Reset", "Cube position reset to origin.")
# Main function to run the UI
def show_translation_app():
window = TranslationApp()
window.setParent(FreeCADGui.getMainWindow(), QtCore.Qt.Window)
window.show()
# Run the application
show_translation_app()
