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ARCHITECTURAL DRAWING & GRAPHICS-III

Sajjad Malik

  • October 24, 2026
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AR203

ARCHITECTURAL DRAWING & GRAPHICS-II

UNIT III

TWO-POINT PERSPECTIVE

Blocks, Curved Surfaces and Residential Applications

Concept diagram: two horizontal edge families converge towards two vanishing points.

B.Arch. II Year / III Semester | Session 2026-27

Unit III Overview

Prescribed Syllabus
Perspectives of simple and complex blocks, curved surfaces; perspectives of residences; etc.

Unit III shifts from the frontal logic of one-point perspective to corner views in which two principal horizontal directions recede from the observer. The study sequence therefore moves from establishing two vanishing directions to simple solids, composite forms, curved surfaces and finally residential architecture.

Learning Objectives

  • Understand the geometric condition that produces two-point perspective.
  • Determine two vanishing points from the object orientation and Station Point.
  • Construct accurate perspectives of simple and complex blocks using plan projection.
  • Develop stepped, recessed, projecting and composite forms without directly measuring perspective depth.
  • Construct circles and cylinders in two-point perspective using an enclosing-square method.
  • Apply two-point perspective to pavilions, small buildings and residential forms with openings and projections.
  • Use line weight, tonal hierarchy and scale references to improve architectural presentation.

Syllabus-to-Study-Note Alignment

Study-note section

Syllabus component

Practice linkage

3.1-3.4

Principles and construction method

Master method / Problems 01-02

3.5

Simple blocks

Exercise-book 05; Problems 01-02

3.6

Complex blocks

Exercise-book 06-07; Problems 03-06

3.7

Curved surfaces

Problem 07

3.8

Furniture / architectural element bridge

Problem 08

3.9

Architectural forms

Exercise-book 08; Problems 09-10

3.10

Residences

Problem 11

3.11

Integrated design application

Problem 12

3.1 Introduction to Two-Point Perspective

Two-point perspective is a perspective system in which two principal families of horizontal parallel lines recede in different directions and converge towards two separate Vanishing Points, generally located on the Horizon Line. It is most commonly used when an object or building is viewed from a corner rather than directly from the front.

Core Rule
Verticals remain vertical. One horizontal edge family converges to VP₁; the second horizontal edge family converges to VP₂. Both horizontal VPs lie on the Horizon Line when those spatial directions are horizontal.

Two-point perspective is particularly useful for building exteriors because it can show two adjoining façades simultaneously and communicate the mass, depth and corner condition of an architectural form.

3.2 Conditions for Two-Point Perspective

Principal direction

Behaviour in two-point perspective

Vertical edges

Remain vertical in standard two-point perspective

Horizontal direction 1

Converges towards VP₁

Horizontal direction 2

Converges towards VP₂

Horizon Line

Carries both horizontal vanishing points

Nearest corner / vertical edge

Often used as the principal true-height reference when it touches PP

Object orientation

Usually neither principal horizontal face is parallel to PP

The number of vanishing points is related to the number of principal spatial directions that recede from the observer, not to the complexity of the object. A very simple block may use two vanishing points, while a complex object can still be constructed from the same two horizontal directions.

3.3 Determining the Two Vanishing Points

The vanishing points are obtained from the plan. For each family of horizontal parallel edges, draw a line through the Station Point parallel to that spatial direction. Where the line meets the Picture Plane gives the plan location of the corresponding vanishing direction; project that point to the Horizon Line to obtain the Vanishing Point.

Important Rule
SP ∥ Direction 1 → v₁ on PP → project to VP₁ on HL.  SP ∥ Direction 2 → v₂ on PP → project to VP₂ on HL.

3.4 Master Construction Method

  1. 1. Draw the Picture Plane and place the object plan in the specified orientation.
  2. 2. Locate the Central Plane and Station Point at the given distance from PP.
  3. 3. From SP draw lines parallel to the two principal horizontal object directions to obtain v₁ and v₂ on PP.
  4. 4. Draw visual rays from SP to every important plan corner; mark their piercing points on PP.
  5. 5. Draw the Ground Line and Horizon Line according to the given eye height.
  6. 6. Project v₁ and v₂ vertically to HL to obtain VP₁ and VP₂.
  7. 7. Locate the nearest ground corner in the perspective field and draw its two receding edges towards VP₁ and VP₂.
  8. 8. Use vertical projectors from the plan piercing points to locate the remaining base corners.
  9. 9. Complete the base by joining corresponding directions towards the opposite VP.
  10. 10. Transfer true height on a suitable vertical edge, preferably one touching PP, then complete the top edges towards VP₁ and VP₂.
  11. 11. For recesses, steps, openings and projections, locate every important plan point first; do not guess perspective dimensions.
  12. 12. Keep construction lines light and darken only the final visible edges.

Memory Sequence
PLAN → SP → TWO VANISHING DIRECTIONS → VISUAL RAYS → HL/GL → BASE → TRUE HEIGHT → COMPLETE FORM

3.5 Perspective of Simple Blocks

The rectangular prism is the basic two-point-perspective exercise. Once students understand how a single corner, two edge directions and a true height generate a complete box, the same logic can be reused for most architectural forms.

The supplied exercise booklet includes Exercise 05, a rectangular prism with a 50 mm × 30 mm base and 55 mm height, with one vertical edge in PP and the longer base edge inclined at 45° to PP. This is a direct Unit-III application because the two horizontal edge families recede in different directions.

  • Locate the nearest vertical edge and both VPs first.
  • Never measure the 50 mm or 30 mm directly along receding perspective lines.
  • Use plan visual rays to locate the far corners.
  • Use the edge on PP as the true-height line when available.

3.6 Complex and Composite Blocks

Complex forms should be interpreted as combinations or modifications of simple volumes. The most reliable workflow is to construct an overall bounding volume first, then add or subtract features through plan-projected points.

Operation

Construction idea

Stacking

Construct lower block first; locate upper footprint on the top plane; raise the second height.

Stepping

Divide the plan direction; transfer step heights on a true-height vertical; connect to the appropriate VP.

Recess

Locate opening limits in plan and elevation; send the recess depth towards the opposite VP.

Projection

Establish the projecting footprint in plan before raising or lowering its edges.

Subtraction / L-shape

Project every plan corner; reconstruct the outline by alternating VP₁ and VP₂ directions.

Exercise-book Exercise 06 (square pyramid) and Exercise 07 (three-step model) are useful source problems for this stage. Their inclined base orientations produce the two-directional recession characteristic of Unit III.

3.7 Curved Surfaces in Two-Point Perspective

A circle viewed in perspective generally appears as an ellipse. Directly sketching the ellipse by eye is unreliable when geometric accuracy is required. A common method is to first enclose the circle within a square, construct that square in perspective, transfer key points and then draw the smooth perspective ellipse through them.

  1. 1. Draw the circle in plan inside a square of side equal to the circle diameter.
  2. 2. Mark side midpoints and, where greater accuracy is required, additional diagonal points.
  3. 3. Construct the square in two-point perspective on the required plane.
  4. 4. Transfer the circle points into the perspective quadrilateral.
  5. 5. Draw a smooth ellipse through the transferred points.
  6. 6. For a vertical cylinder, raise the required height, construct the second ellipse and join the visible vertical tangents.

Graphic Caution
The ellipse is not an arbitrary oval. Its size and orientation are controlled by the perspective of the enclosing square.

3.8 Furniture and Architectural Elements as an Intermediate Exercise

Although Unit III emphasises blocks, curved surfaces and residences, a table or simple pavilion is a useful bridge between pure geometric solids and architecture. It forces students to repeat the same two vanishing directions across several small elements while keeping vertical supports aligned.

  • Start with an overall bounding box.
  • Locate repeated legs/columns in plan.
  • Project all horizontal edges towards the correct VP.
  • Transfer heights from common level lines rather than estimating each element independently.

3.9 Two-Point Perspective of Architectural Forms

At architectural scale, the same geometric rules remain unchanged. The main difference is the number of secondary features: openings, porch projections, parapets, roof slabs, columns and level changes. These should be added only after the main building mass is correct.

  1. 1. Construct the main building block from the plan and true height.
  2. 2. Locate doors and windows in plan; project their vertical limits into the perspective field.
  3. 3. Transfer sill, lintel and parapet heights from suitable reference verticals.
  4. 4. Use VP₁ for all edges parallel to the first façade direction and VP₂ for the second façade direction.
  5. 5. Construct canopies, projections or recesses from their plan footprints rather than by visual approximation.
  6. 6. Add rendering only after all construction geometry is verified.

Exercise-book Exercise 08, a shed with its long horizontal edges inclined at 45° to PP, is an appropriate transition from blocks to a complete architectural form.

3.10 Perspective of Residences

A residence combines nearly all Unit-III skills: multiple masses, openings, porch projections, parapets or roofs, steps, human scale and landscape elements. The correct approach is hierarchical: solve the main mass first, then secondary architectural features, then presentation details.

Stage

Priority

1. Main massing

Overall plan, corner position, VPs, storey height

2. Secondary masses

Porch, bay, stair, balcony, projections

3. Openings

Door/window locations, sill and lintel levels

4. Roof / parapet

Complete roof edges or parapet lines to correct VP

5. Scale & context

Human figures, vegetation, paving, furniture/vehicles as needed

6. Graphic finish

Line hierarchy, material tone, shadows and sciography

3.11 Rendering and Graphic Presentation

Graphic element

Recommended treatment

Nearest visible edges

Heavier line weight

Secondary building edges

Medium line weight

Construction / projection lines

Very light and removable

Distant edges / background

Light line or reduced contrast

Curved surfaces

Smooth continuous contour; avoid faceted ellipse

Shadows / sciography

Consistent light direction; use to reinforce volume, not hide errors

3.12 Common Errors in Two-Point Perspective

Common error

Correction

Using the wrong VP for an edge

Classify every horizontal edge by its spatial direction before drawing it.

Measuring depth directly on receding lines

Use plan visual rays, measuring methods or perspective subdivisions.

Placing VP₁ and VP₂ arbitrarily

Derive them from SP using lines parallel to the two plan directions.

Tilting verticals

Vertical edges remain vertical in standard two-point perspective.

Constructing openings before the main mass

Complete the main block first, then locate secondary features.

Drawing circles as casual ovals

Use an enclosing square and transferred points.

Excessive distortion

Choose a reasonable SP and keep the object within a comfortable field of view.

Over-dark construction lines

Use light guides; strengthen only the final object.

3.13 Source Exercise-Book Problems Appropriate to Unit III

The following problems from the supplied exercise booklet are especially appropriate for Unit III because their principal horizontal directions are inclined to the Picture Plane and therefore generate two-directional recession.

Exercise

Problem focus

Exercise 05

Rectangular prism; 50 × 30 base, 55 high; longer edge 45° to PP.

Exercise 06

Square pyramid; base edges equally inclined to PP.

Exercise 07

Three-step model; longer edge 30° to PP.

Exercise 08

Shed; long horizontal edges 45° to PP; complete architectural form.

3.14 Progressive Two-Point Perspective Problem Bank (01-12)

The following 12 problems are the progressive teaching set developed earlier for this course. They move from a basic prism to composite and curved forms and finally to architectural/residential applications. Where a viewer location was not originally specified, a practical Station Point / Central Plane value has been standardised here so that the exercise is directly usable in class.

Problem 01 – Rectangular Prism

Problem Statement
A rectangular prism measuring 60 mm × 40 mm × 35 mm high rests on the Ground Plane. One vertical edge touches the Picture Plane. The 60 mm side is inclined at 30° to PP. The Station Point is 75 mm in front of PP and 60 mm above GP. The Central Plane passes 25 mm to the right of the vertical edge touching PP. Construct the two-point perspective of the prism.

Learning focus: Establish VP₁ and VP₂ and understand the basic two-directional convergence.

Problem 02 – Square Prism

Problem Statement
A square prism having a base of 45 mm × 45 mm and a height of 60 mm rests on GP. One vertical edge touches PP and the base edges are equally inclined to PP. The Station Point is 70 mm in front of PP and 65 mm above GP. The Central Plane passes 20 mm to the right of the touching edge. Construct its two-point perspective.

Learning focus: Balanced 45°-45° orientation and symmetrical vanishing directions.

Problem 03 – Three-Step Composition

Problem Statement
Draw the two-point perspective of a three-step block having an overall length of 60 mm, width 45 mm and total height 45 mm. Each step has a tread of 20 mm and a riser of 15 mm. One front vertical edge touches PP and the longer direction is inclined at 30° to PP. The Station Point is 80 mm in front of PP and 60 mm above GP. Take the Central Plane 25 mm to the right of the touching edge.

Learning focus: Repeated divisions, height transfer and stepped geometry.

Problem 04 – L-Shaped Solid

Problem Statement
An L-shaped solid is formed from a rectangular block 60 mm × 45 mm × 35 mm high by removing a 30 mm × 20 mm portion from one corner of the plan. One outer vertical edge touches PP and the 60 mm side is inclined at 30° to PP. The Station Point is 85 mm in front of PP and 65 mm above GP. Take the Central Plane 25 mm to the right of the touching edge. Construct its two-point perspective.

Learning focus: Project every corner of an irregular plan rather than guessing the final shape.

Problem 05 – Composite Blocks of Different Heights

Problem Statement
A base block measuring 70 mm × 45 mm × 20 mm high carries another rectangular block measuring 35 mm × 25 mm × 30 mm high centrally on its top surface. One vertical edge of the lower block touches PP and its longer side is inclined at 30° to PP. The Station Point is 90 mm in front of PP and 65 mm above GP. Take the Central Plane 25 mm to the right of the touching edge. Draw the complete two-point perspective.

Learning focus: Locate a secondary footprint on an upper perspective plane and transfer multiple heights.

Problem 06 – Block with Recessed Opening

Problem Statement
A rectangular block measuring 70 mm × 40 mm × 50 mm high has a rectangular recess 20 mm wide × 25 mm high × 10 mm deep on its longer face. The recess is centrally located on that face. One vertical corner of the main block touches PP and the longer side is inclined at 30° to PP. The Station Point is 80 mm in front of PP and 60 mm above GP. Take the Central Plane 25 mm to the right of the touching edge. Construct the two-point perspective.

Learning focus: Openings, recess depth and transfer of vertical levels.

Problem 07 – Block with Cylindrical Element

Problem Statement
A rectangular base measuring 60 mm × 45 mm × 20 mm high supports a vertical cylinder of 25 mm diameter and 35 mm height, placed centrally on the top surface. The longer side of the base makes 30° with PP. One vertical edge of the base touches PP. The Station Point is 80 mm in front of PP and 60 mm above GP; take the Central Plane 25 mm to the right of the touching edge. Construct the perspective using an appropriate enclosing-square method for the circular surfaces.

Learning focus: Curved surfaces, perspective ellipse and cylinder construction.

Problem 08 – Simple Furniture – Table

Problem Statement
Draw the two-point perspective of a table having a top 60 mm × 40 mm, thickness 5 mm and overall height 45 mm. The four legs are 5 mm × 5 mm in section. One corner of the table is nearest to the observer and the longer side is inclined at 30° to PP. Take SP 80 mm in front of PP, 60 mm above GP and CP 25 mm to the right of the nearest corner.

Learning focus: Repeated vertical elements and bounding-box construction.

Problem 09 – Architectural Pavilion

Problem Statement
A small open pavilion has an overall plan of 70 mm × 50 mm. Four corner columns measuring 6 mm × 6 mm support a roof slab at a height of 50 mm. The roof slab is 5 mm thick and projects 5 mm beyond the columns on all sides. One corner of the pavilion touches PP and the longer side is inclined at 30° to PP. Take SP 90 mm in front of PP, 65 mm above GP and CP 25 mm to the right of the touching corner. Construct its two-point perspective.

Learning focus: Columns, roof projection, repeated supports and architectural scale.

Problem 10 – Single-Storey Building with Openings

Problem Statement
A simple single-storey building measures 80 mm × 55 mm × 45 mm high with a 10 mm parapet. One vertical corner touches PP and the 80 mm wall is inclined at 30° to PP. Provide a 20 mm × 30 mm entrance door on the longer face and a 20 mm × 15 mm window with 15 mm sill height on each visible face. Take SP 100 mm in front of PP, 70 mm above GP and CP 25 mm to the right of the touching corner. Construct the two-point perspective.

Learning focus: Façade openings, sill/lintel levels and parapet construction.

Problem 11 – Residence with Entrance Porch

Problem Statement
Construct the two-point perspective of a single-storey residence having a main block 90 mm × 60 mm × 45 mm high. Provide an entrance porch 30 mm wide × 20 mm projection supported by two columns, and a 10 mm parapet above the roof. Add suitable doors and windows using proportional subdivisions. Position one corner of the main building on PP with the longer side at 30° to PP. Take SP 110 mm in front of PP, 70 mm above GP and CP 30 mm to the right of the touching corner.

Learning focus: Residential massing, porch projection and façade articulation.

Problem 12 – Integrated Architectural Composition

Problem Statement
Design a small architectural composition consisting of at least three interconnected rectangular masses of different heights, one projecting element, one recessed element and one curved surface. Prepare a simple dimensioned plan first and then construct its two-point perspective from a suitable corner viewpoint. Add human figures, vegetation and appropriate sciography to communicate scale and depth.

Learning focus: Design synthesis: combine all Unit-III skills in one controlled perspective composition.

3.15 Quick Revision

Two-Point Perspective at a Glance
Two horizontal VPs • both on HL for horizontal directions • verticals remain vertical • derive VPs from SP and plan directions • use plan visual rays for depth • transfer true heights on suitable verticals • circles require perspective ellipses • solve the main building mass before openings and projections.

Review Questions

  1. 1. Define two-point perspective and explain when it is preferred over one-point perspective.
  2. 2. Describe the plan method used to obtain VP₁ and VP₂ from the Station Point.
  3. 3. Why should receding dimensions not be measured directly on the perspective lines?
  4. 4. Explain the construction sequence for a rectangular prism with one vertical edge touching PP.
  5. 5. Describe how a stepped or L-shaped block should be constructed in two-point perspective.
  6. 6. Explain the enclosing-square method for a circle or cylinder in perspective.
  7. 7. How are doors and windows accurately positioned on two visible building façades?
  8. 8. Describe the correct construction hierarchy for a residential two-point perspective.

Short MCQ Revision

Question

Answer

How many principal horizontal vanishing points are normally used?

Two

Where are horizontal VP₁ and VP₂ located?

On the Horizon Line

What happens to verticals in standard two-point perspective?

They remain vertical

How is VP₁ derived?

Through SP draw a line parallel to Direction 1; project its PP intersection to HL

How should a circle be constructed accurately?

By projecting an enclosing square and transferring points

What should be solved first in a residence?

The main building mass / bounding geometry

Suggested Submission / Practice Sheet Sequence

Sheet

Problem(s)

Purpose

1

Problems 01-02

Simple prism fundamentals and two VPs

2

Problems 03-04

Steps and irregular plan

3

Problems 05-06

Composite block and recess

4

Problem 07

Curved surface / cylinder

5

Problem 08

Furniture / repeated verticals

6

Problems 09-10

Pavilion and small building

7

Problem 11

Residential perspective

8

Problem 12

Integrated architectural composition

End of Unit III

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