Chapter 2: 3D Fundamentals and Coordinate Systems

Learning Objectives

• Understand the 3D spatial coordinate system
• Master object transformation operations (move, rotate, scale)
• Learn object selection and editing modes
• Understand local and global coordinate systems
• Master precision modeling tools and alignment functions

Detailed Knowledge Points

2.1 3D Spatial Coordinate System

2.1.1 Cartesian Coordinate System

In 3D space, we use a three-dimensional Cartesian coordinate system to locate objects:

Y-axis (Green)
↑
│
│
└────→ X-axis (Red)
/
/
Z-axis (Blue)

Coordinate Axis Description:

• X-axis (Red): Left-right direction, positive direction is to the right
• Y-axis (Green): Front-back direction, positive direction is forward
• Z-axis (Blue): Up-down direction, positive direction is up

Blender Coordinate System Features

• Blender uses a right-handed coordinate system
• The Z-axis is the up direction (unlike some software where the Y-axis is up)
• The origin (0, 0, 0) is at the center of the scene

2.1.2 Coordinate System Types

Global Coordinate System:

• Fixed world coordinate system
• All objects are located relative to this coordinate system
• The direction of the coordinate axes never changes

Local Coordinate System:

• Each object has its own coordinate system
• Changes direction as the object rotates
• Convenient for operations relative to the object itself

View Coordinate System:

• Relative to the current view
• Changes as the viewport rotates
• Convenient for operations from the current perspective

2.2 Basic Transformation Operations

2.2.1 Grab/Move Operation

Basic Move:

G         # Activate move tool, follows the mouse
G + X     # Constrain to X-axis move
G + Y     # Constrain to Y-axis move
G + Z     # Constrain to Z-axis move

# Precise Move
G + X + 2   # Move 2 units along the X-axis
G + Y + -1  # Move 1 unit in the negative Y-axis direction

# Plane Move (excluding an axis)
G + Shift + Z  # Move on the XY plane (excluding Z-axis)
G + Shift + X  # Move on the YZ plane (excluding X-axis)

Move Example Exercise:

# Create a simple scene layout
# 1. Keep the default cube at the origin
# 2. Add a sphere: Shift + A → Mesh → UV Sphere
# 3. Move the sphere: G + X + 3 (move 3 units to the right)
# 4. Add a cylinder: Shift + A → Mesh → Cylinder
# 5. Move the cylinder: G + Y + 3 (move 3 units forward)

2.2.2 Rotate Operation

Basic Rotate:

R         # Activate rotate tool
R + X     # Rotate around X-axis
R + Y     # Rotate around Y-axis
R + Z     # Rotate around Z-axis

# Precise Rotate
R + Z + 45  # Rotate 45 degrees around the Z-axis
R + X + 90  # Rotate 90 degrees around the X-axis

# Incremental Rotate
R + R       # Repeat the last rotation

Pivot Point:

Pivot Point	Shortcut	Description
Bounding Box Center	. (period)	Geometric center of the selected object
3D Cursor	Shift + .	Rotate around the 3D cursor
Individual Origins	Ctrl + .	Each selected object rotates around its own origin
Active Element	Alt + .	Rotate around the last selected object

2.2.3 Scale Operation

Basic Scale:

S         # Uniform scale
S + X     # Scale along X-axis
S + Y     # Scale along Y-axis
S + Z     # Scale along Z-axis

# Precise Scale
S + 2     # Scale up by 2 times
S + 0.5   # Scale down to half
S + -1    # Mirror flip

# Non-uniform Scale
S + Shift + Z  # Scale on the XY plane (without affecting Z)

2.3 Transform Tools and Gizmos

2.3.1 Transform Toolbar

In the toolbar on the left of the 3D viewport:

┌─────────┐
│    ↗    │  Select Tool (W)
├─────────┤
│    ✋   │  3D Cursor Tool (Shift + Right-click)
├─────────┤
│    ↔    │  Move Tool (G)
├─────────┤
│    ↻    │  Rotate Tool (R)
├─────────┤
│    ⊞    │  Scale Tool (S)
├─────────┤
│    ⚒    │  Transform Tool (T)
└─────────┘

2.3.2 Gizmo

The gizmo is the visual transformation tool in the viewport:

Move Gizmo:

• Red arrow: X-axis move
• Green arrow: Y-axis move
• Blue arrow: Z-axis move
• Colored squares: Plane move

Rotate Gizmo:

• Red ring: Rotate around X-axis
• Green ring: Rotate around Y-axis
• Blue ring: Rotate around Z-axis
• White outer ring: Free rotate

Scale Gizmo:

• Colored squares: Uniform scale
• Colored lines: Single-axis scale

2.4 Precision Modeling Tools

2.4.1 Numeric Input

Precise Transform Input:

# Enter numeric values directly during a transform operation
G + X + Tab  # Switch to numeric input mode
# Then enter a specific value, e.g., 2.5

# Use expressions
S + Tab  # Enter numeric input
# Can enter: *2 (multiply by 2) or /3 (divide by 3) or +1.5 (add 1.5)

2.4.2 Snapping Tool

Snap Settings:

# Enable/disable snapping
Shift + Tab  # Toggle snapping

# Snap type (set in the header bar)
- Increment: Snap to grid
- Vertex: Snap to vertex
- Edge: Snap to edge
- Face: Snap to face
- Volume: Snap to volume

Snap Options:

Option	Description	Use Case
Closest	Snap to the closest target	General use
Center	Snap to the center of the target	Alignment operations
Median	Snap to the median of the selection	Used with multiple selections
Active	Snap to the active element	Precise alignment

2.4.3 Proportional Editing

O  # Enable/disable proportional editing

# Proportional editing types
- Smooth: Smooth influence
- Sphere: Spherical influence
- Root: Root-like influence
- Sharp: Sharp influence
- Linear: Linear influence
- Constant: Constant influence

# Adjust influence range
Mouse wheel  # Adjust influence radius in proportional editing mode

2.5 Switching Coordinate Systems

2.5.1 Transform Orientation

You can switch the transform orientation in the 3D viewport header bar:

Global     # Use world coordinate system
Local      # Use object's local coordinate system
Normal     # Use face normal coordinate system
Gimbal     # Use gimbal coordinate system
View       # Use view coordinate system
Cursor     # Use 3D cursor coordinate system

2.5.2 Transform Pivot Point

The transform pivot point determines the center of the transformation:

Pivot Point Types:

# Bounding Box Center
# Suitable for: General transform operations

# 3D Cursor
# Suitable for: Rotating around a specific point

# Individual Origins
# Suitable for: Transforming multiple objects individually

# Median Point
# Suitable for: The center point of multiple selected objects

# Active Element
# Suitable for: Using the last selected element as a reference

2.6 Advanced Selection Tools

2.6.1 Selection Tools

Basic Selection:

A          # Select all
Alt + A    # Deselect all
Ctrl + I   # Invert selection
H          # Hide selected
Alt + H    # Unhide all
Shift + H  # Hide unselected

Box and Circle Select:

B          # Box select tool
C          # Circle select tool (mouse wheel adjusts size)
Alt + B    # Box select view clipping

2.6.2 Select Similar

Shift + G  # Select similar menu
- Type: Select by type
- Material: Select by material
- Color: Select by color
- Dimensions: Select by dimensions

2.7 3D Cursor and Origin

2.7.1 3D Cursor

The 3D cursor is a positioning tool in the scene:

Shift + Right-click  # Place 3D cursor
Shift + S     # Snap menu
- Cursor to Selected: Cursor to selected
- Selection to Cursor: Selection to cursor
- Cursor to Center: Cursor to center
- Cursor to Grid: Cursor to grid

2.7.2 Origin Operations

# Set origin position
Ctrl + Alt + Shift + C  # Origin menu
- Geometry to Origin: Geometry to origin
- Origin to Geometry: Origin to geometric center
- Origin to 3D Cursor: Origin to cursor
- Origin to Center of Mass: Origin to center of mass

2.8 Practical Exercises

Exercise 1: Understanding Coordinate Systems

Exercise Goal

Understand the differences and use cases of different coordinate systems

# 1. Create three cubes
# 2. Arrange them in an L-shape
# 3. Rotate the middle cube by 45 degrees
# 4. Move the rotated cube in both global and local coordinate systems
# 5. Observe the difference in operation

Steps:
1. Delete the default cube
2. Shift + A to add a cube at (0, 0, 0)
3. Shift + D to duplicate, move to (2, 0, 0)
4. Shift + D to duplicate again, move to (0, 2, 0)
5. Select the cube at (2, 0, 0)
6. R + Z + 45 to rotate 45 degrees
7. Switch coordinate systems in the header bar and observe the gizmo change
8. Move this cube using both global and local coordinate systems

Exercise 2: Precision Modeling Exercise

# Make a simple table model
# Requirements: Tabletop 2x1x0.1, table legs height 0.8

# Tabletop creation
1. Add a cube
2. S + X + 1 (scale to 2 along X-axis)
3. S + Y + 0.5 (scale to 1 along Y-axis)
4. S + Z + 0.05 (scale to 0.1 along Z-axis)
5. G + Z + 0.45 (move up to a suitable position)

# Table leg creation
6. Add a cube for a table leg
7. S + X + 0.05, S + Y + 0.05 (shrink X, Y)
8. S + Z + 0.4 (scale to 0.8 height along Z-axis)
9. G + X + 0.8, G + Y + 0.4 (move to a table corner)
10. Shift + D to duplicate the other three legs

Exercise 3: Comprehensive Transform Tool Application

Important Notes

• Ensure you understand the difference between global and local coordinate systems
• Become proficient in using numeric input for precise transformations
• Use pivot point settings appropriately

# Make a windmill model
# 1. Create a windmill blade (using a plane)
# 2. Duplicate and rotate to create multiple blades
# 3. Create a support pillar
# 4. Assemble into a complete model

Detailed Steps:
1. Delete the default cube
2. Shift + A → Mesh → Plane
3. S + Y + 2 (elongate the plane to form a blade)
4. Set the pivot point to the 3D cursor
5. Shift + S → Cursor to Center (cursor to center)
6. Shift + D to duplicate the blade
7. R + Z + 90 (rotate 90 degrees)
8. Repeat steps 6-7 to create 4 blades
9. Add a cylinder for the support pillar
10. G + Z + -1 (move down)
11. S + Z + 2 (elongate the pillar)

Common Transform Shortcut Summary

Operation	Shortcut	Description
Move	G	Free move
Constrained Move	G + X/Y/Z	Move along an axis
Plane Move	G + Shift + X/Y/Z	Move excluding an axis
Rotate	R	Free rotate
Constrained Rotate	R + X/Y/Z	Rotate around an axis
Scale	S	Uniform scale
Constrained Scale	S + X/Y/Z	Scale along an axis
Toggle Snap	Shift + Tab	Enable/disable snapping
Proportional Editing	O	Enable/disable proportional editing
3D Cursor	Shift + Right-click	Place cursor

Transform Tool Settings

2.9 Transform Settings Panel

In the Transform tab of the Properties panel:

Location:

• X, Y, Z coordinate values
• Can directly input precise numeric values

Rotation:

• Euler angles: X, Y, Z axis rotation angles
• Axis-angle: Rotation axis and angle
• Quaternion: Four-dimensional rotation representation

Scale:

• X, Y, Z axis scale factors
• Link icon: Maintain proportional scaling

2.10 Object Relationships and Hierarchy

2.10.1 Parent-Child Relationship

# Establish a parent-child relationship
1. Select the child object first
2. Then select the parent object (Shift + Left-click)
3. Ctrl + P → Object (Keep Transform)

# Remove parent-child relationship
Alt + P → Clear Parent

Parent-Child Relationship Features:

• Child object follows the parent object's transformations
• Child object's coordinates are relative to the parent object
• Forms a hierarchical structure for easy management

2.10.2 Collection Management

# Create a collection
M  # Move to collection menu
Shift + A  # Create a new collection

# Collection operations
- Hide/show collection
- Enable/disable collection selection
- Instance collection

Learning Suggestions

1. Understand Coordinate Systems: The difference between global and local coordinate systems is fundamental to 3D work
2. Master Transform Operations: The three basic operations G, R, S must be very proficient
3. Master Precise Control: Learn to use numeric input and snapping tools
4. Develop Spatial Thinking: Observe and operate objects from different angles
5. Use Helper Tools: 3D cursor, proportional editing, etc., can greatly improve efficiency

By completing this chapter, you should be able to:

• Understand the basic concepts of 3D space
• Use various transform tools proficiently
• Precisely control the position, rotation, and scale of objects
• Understand the use cases of different coordinate systems

These skills are the foundation for all subsequent 3D operations and must be mastered.