📐 Geometric Projections

Projection is a method of representing a three-dimensional object on a two-dimensional drawing surface (paper, screen) using straight lines drawn from the object to an imaginary plane.

The three main types of projections used in architecture, planning, and engineering are:

Orthographic Projection
Isometric Projection
Perspective Projection

1️⃣ Orthographic Projection

Definition: A method of representing objects by projecting perpendicular lines (orthogonal) from the object to the projection plane.
Characteristics:
- Shows exact shape and size.
- No distortion.
- Multiple views (front, top, side) needed to fully describe object.
Applications: Engineering drawings, building plans, technical blueprints.

Orthographic views of different dimensions:

1D object (a line) → Appears as a line or point depending on orientation.
2D object (a square, triangle, circle) → Shows true shape (e.g., square as square, circle as circle) when parallel to projection plane.
3D object (cube, cylinder, cone) → Represented using multiple views:
- Front view
- Top view
- Side view

📌 Example: A cube in orthographic projection is shown as three separate 2D views (square front, square top, square side).

2️⃣ Isometric Projection

Definition: A type of axonometric projection where the object is tilted so its three principal axes make equal angles (120°) with each other.
Characteristics:
- Provides a pictorial 3D view.
- Scale along each axis is equal, so proportions are preserved.
- Parallel lines remain parallel (no vanishing point).
Applications: Design visualization, engineering drawings, exploded views.

Isometric representation of different dimensions:

1D (line) → Drawn along one of the isometric axes at 120°.
2D (plane figure) → A square becomes a rhombus; a circle appears as an ellipse.
3D (solid figure) → Cube appears as an equal-sided rhombus structure; cylinder drawn with elliptical bases.

📌 Example: A cube in isometric looks like three visible rhombus faces meeting at 120°.

3️⃣ Perspective Projection

Definition: A projection method where visual rays converge at a point (the eye or station point) and intersect the projection plane.
Characteristics:
- Mimics human vision.
- Objects appear smaller as distance increases.
- Provides realistic depth.
- Has vanishing points depending on type.
Applications: Architecture, urban design, interior design, landscape planning.

Types of Perspective:

One-point perspective → Used for roads, railway tracks, corridors; parallel lines converge at a single vanishing point.
Two-point perspective → Used for showing corners of buildings; two sets of parallel lines converge at two different vanishing points.
Three-point perspective → Used for tall buildings or aerial views; vertical lines also converge at a third vanishing point.

Perspective of dimensions:

1D line → Appears as a line receding toward a vanishing point.
2D shape → A square looks like a trapezium if tilted away; a circle appears as an ellipse.
3D object → A cube appears realistic, with depth shown by receding edges toward vanishing points.

📌 Example: A cube in two-point perspective shows vertical edges true, but horizontal edges converge at two vanishing points.

🔑 Comparison of Projection Methods

Feature	Orthographic Projection	Isometric Projection	Perspective Projection
Nature	Technical, accurate	Pictorial, measurable	Realistic, visual
Lines	Parallel → parallel	Parallel → parallel	Parallel → converge
Scale	True scale	Foreshortened equally	Diminishes with depth
Use	Working drawings	Design visualization	Architectural renderings

✅ In summary:

Orthographic → exact, technical, needs multiple views.
Isometric → pictorial 3D, equal foreshortening, no vanishing point.
Perspective → realistic, mimics human vision, vanishing points.