Perspectiva Cónica de 2 Puntos de Fuga a partir de las Proyecciones Ortogonales en Tercer Cuadrante

Linear or Conical System Exercise

Introduction to the Exercise

• The video introduces a linear or conical system exercise, focusing on drawing a perspective of an organized set of lenga pieces. The arrangement adheres to a module based on the shortest side, which is indicated as 'y' .

Dimensions and Layout

• The lenga pieces have specific dimensions: 0.5 meters for the short side, 1 meter for the intermediate side, and 3 meters for the long side. This setup aligns with a grid of 50 cm that will aid in creating the perspective view .

Establishing Perspective Points

• A plan is drawn at angles of 30 and 60 degrees relative to the base grid. The viewer's point of view is established at a perpendicular distance from this grid, specifically at 4 cm away from point 'p' .

Drawing Focal Points

• Two points of escape (f1 and f2) are determined by drawing lines parallel to both horizontal and vertical elements from point 'p'. These lines intersect with the picture plane to establish critical focal points for perspective drawing .

Working with Scale

• The exercise operates on a scale of 2:1. All measurements taken must be doubled when transferring them into perspective drawings. For instance, if establishing height based on average human stature (approximately 175 cm), this measurement will also be scaled accordingly .

Constructing Perspective Lines

Horizon Line and Ground Line

• A ground line is drawn horizontally across the layout while maintaining its relationship with other established points. The horizon line is then created parallel to this ground line, extending towards the right side of the drawing area .

Utilizing Escape Points

• Point f1 serves as an initial reference for further measurements along the ground line. Distances between escape points f1 and f2 are transferred onto this line twice due to working in scale, ensuring accurate representation in perspective drawings .

Establishing Grid Structure

• As part of constructing a square mesh within the layout, distances between numbered points (1, 2, and 3) are marked accurately along both horizon and ground lines. This ensures that all elements align correctly within their respective perspectives .

Finalizing Perspective Drawing

Completing Square Mesh

• To finalize construction, additional measures are taken by duplicating distances between key points (e.g., from point two to three). This step ensures that all parts fit cohesively within an eight-part division using Thales' theorem .

Marking Final Connections

• Finally, connections are made between point two and both escape points f1 and f2 to outline edges clearly visible in plan view. Additional connections complete other necessary edges leading back into square formation .

This structured approach allows viewers to follow along easily while understanding how each step contributes toward achieving an accurate perspective representation in architectural design exercises.

Drawing a Square Grid in Perspective

Importance of Precision in Drawing

• The use of a square and set square is crucial for ensuring segments are equal, allowing for accurate division into eight equal parts.

• As dimensions recede in perspective, they appear smaller; this principle is essential when drawing lines that will intersect at various points.

Constructing the Grid

• A diagonal line is drawn across the square to create intersections with previously drawn lines, establishing vertical connections within the grid.

• Vertical lines are extended from specific points to measure height accurately, maintaining true scale as indicated on the screen.

Height Measurement and Scaling

• Heights are transported vertically twice from a reference point, adhering to a 2:1 scale ratio as noted in the lower right corner of the display.

• The drawings utilize an American system (third quadrant), with plant views positioned above to assist in visualizing heights accurately.

Establishing Vertical Connections

• Heights are transferred from all four vertices of the square, creating varying heights based on their depth relative to perspective points F1 and F2.

• The top surface of a container box is established through these vertical measurements, aiding in spatial representation.

Finalizing Piece Dimensions

• Each small square's height is measured using a compass for accuracy; two squares equate to one unit in perspective due to scaling adjustments.

• Markings indicate different heights corresponding to each piece without needing full mesh drawings on cube faces; focus shifts directly onto individual pieces.

Defining Piece Boundaries

Drawing Vertical Lines

• Two pieces reaching up to height three are connected back to point F1, establishing clear boundaries for upper sections.

• A definitive vertical line is drawn after moving two squares rightward, marking width accurately against existing structures.

Completing Structural Elements

• Additional vertical lines extend upward until reaching specified heights while converging towards point F1 for clarity in design.

• Faces of pieces are finalized by extending lines toward F2 and ensuring proper alignment with previously established dimensions.

Complexity of Layered Drawings

• When elements do not reach the edge of squares, additional care must be taken to project heights correctly across multiple surfaces until they meet at designated points.

• The upper vertex's position is determined by connecting it back through point F1 for accurate placement within the overall structure.

Drawing a 3D Perspective of a Piece

Initial Setup and Drawing the Rectangle

• The drawing begins with outlining a rectangle in perspective, using a fine black line for the vertical part that extends to point F2. This forms the basis of the fugue rectangle for the piece being represented.

• The height measurements are taken into account, specifically heights one and three, which are brought towards F2 to establish accurate dimensions.

Establishing Faces and Dimensions

• A face is established that touches the limits of the square base, simplifying its placement within the overall structure. This face corresponds to a side view of the rectangle as seen laterally.

• Points from this face are transferred to F1, allowing for further detailing of the piece being drawn with thicker lines once intersections are identified. This marks progress in defining horizontal surfaces.

Completing Horizontal Surfaces

• The horizontal surface is finalized with clear markings indicating where it intersects with other components of the drawing, ensuring clarity in representation. A thick line is used for definitive outlines after initial sketches were made with finer lines.

• Additional pieces are drawn above this surface, requiring vertical lines to be established from specific points on previously defined areas to maintain coherence in perspective.

Detailing Vertical Elements

• As vertical elements are added, care is taken to ensure they align correctly within their spatial context; these include additional fugues leading up to F1 without changing planes but marking ends clearly.

• A horizontal piece supported by two previously drawn structures is located accurately through careful alignment on an external grid or mesh system before finalizing its position in space through fugue techniques towards F1.

Finalizing Details and Perspectives

• Vertical lines close off faces that may present challenges due to their retraction relative to outer cubes; however, these complexities do not hinder overall representation efforts significantly.

• The completion involves refining all remaining lines and ensuring visibility across all parts of the drawing while addressing any last-minute adjustments needed for accuracy in perspective views presented at different angles (dihedral views).

Conclusion and Viewer Engagement