3D Surface The modelling of 3D surfaces actually consists of two main stages: drawing of defining curves or generatrixes and formation of surface. The surface is 3D mesh. It is sometimes useful to enhance the quality of your 3D meshes by controlling their density in either one or two directions (called the M direction and N direction). The density of a RULESURF mesh or a TABSURF mesh may be controlled in one direction only via the SURFTAB1 system variable (higher values giving denser meshes). The density of a EDGESURF mesh or REVSURF mesh may be controlled in both M direction and N direction via the system variables SURFTAB1 and SURFTAB2. When using EDGESURF, the M direction is defined as the direction of the first edge selected. When using REVSURF, the M direction is defined as the circumferential direction of the revolved surface. Before creating a surface model it is recommended to turn on such toolbars: Surface, UCS, View, Shade. Use command TOOLBAR (to)

Task. Draw a surface model of a chair according to given frame axis dimensions. Draw a chair seat and a seat back in a free style.

cross-section of chair frame

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As a chair frame is a symmetrical object, you should draw half of it and then make a mirror copy. 1. Use command LAYERS (la) to create new layers AXIS, CURVE, SURFACE and SURFACE2. Set layer AXIS current. 2. Draw contour of the chair frame side perimeter using commands LINE and ARC.

3. Rotate drawn perimeter in space. Command: rotate3d Select objects: select all elements of drawn perimeter Select objects: â&#x2020;&#x201C; Specify first point on axis: select point 1 (end) Specify second point on axis: select point 2 (end) Specify rotation angle or [Reference]: 90

4. Draw the underneath part of a chair frame. Command: LINE Specify first point: pick any point Specify next point or [Undo]: @0,-15 Specify next point or [Undo]: â&#x2020;&#x201C; Command: ARC Specify start point of arc or[CEnter]:pick last endpoint of drawn line Specify second point of arc or [CEnter/ENd]: en Specify end point of arc: @10,-10 Specify center point of arc or [Angle/Direction/Radius]: r Specify radius of arc: 10

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Command: MOVE Select objects: pick last drawn line and arc Select objects: ↓ Specify base point or displacement: pick point 3 (end) Specify second point of displacement: pick point 1 (end)

5. Draw the upper part of a chair frame.

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Change UCS – raise it to the point 3. For that purpose use command (UCS Origin) Draw line and arc in an analogous way like underneath part was drawn.

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Return UCS World

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Now, when spatial axis of the chair frame is ready it should be coved with the surface. First of all define the needed curves of the surface. 6. Set layer CURVE current. 7. Set UCS in due position. Use buttons around X axes:

(UCS Origin) and pick point 4. Then rotate UCS

(X Axis Rotate UCS); rotate it 90 degrees.

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8. Draw circle. Command CIRCLE (c) (center point 4 – an endpoint of line, radius 2).

9. Set layer SURFACE current. 10. Return UCS World . 11. Set SURFTAB1 and SURFTAB2variables value 12. 12. Create tabulated surface Command: tabsurf Select object for path curve: pick blue circle Select object for direction vector: pick orange line

result

The first surface is drawn. Let’s prepare to define curves for the next, revolved surface. 13. An axis for the revolved surface is needed. It should be perpendicular to arc along which we want to create a revolved surface. Just make a copy of blue line. Command: COPY Select objects: pick blue line above Select objects: ↓ Specify base point or displacement: pick point 5 (end) Specify second point of displacement: pick point 6 (cen)

14. Make revolved surface. Command: revsurf Current wire frame density: SURFTAB1=12 SURFTAB2=12 Select object to revolve: select blue circle

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Select object that defines the axis of revolution: select blue vertical line Specify start angle <0>:↓ Specify included angle (+=ccw, -=cw) <360>: 90

result

NOTE If you can’t select the blue circle, change objects display order in pull-down menu Tools→ Display order→ Bring to front. Then select object you want to be in front of all the rest. You should form in an analogous way the rest parts, revolved and tabulated, surfaces of chair frame and prepare a complete one side of the chair frame presented below.

15. Make a mirror copy to create full frame. Command: mirror3d Select objects: select all drawn elements Select objects: ↓ Specify first point of mirror plane (3 points) or [Object/Last/Zaxis/View/XY/YZ/ZX/3points] <3points>: zx Specify point on ZX plane <0,0,0>: pick point 7 (endpoint of axis) Delete source objects? [Yes/No] <N>:↓

result

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Now, when the chair frame is finished, letâ&#x20AC;&#x2122;s draw the chair seat and seat back. Primarily, defining curves have to be drawn. 16. Move UCS at the due chair seat position. Command: ucs Specify new origin point <0,0,0>: pick line midpoint Command: ucs Specify new origin point <0,0,0>: 0,-25,2

17. Set layer CURVE current. 18. Look at your object from above and draw lines according to measures. Command: plan Enter an option [Current ucs/Ucs/World] <Current>:â&#x2020;&#x201C;

19. Fillet due lines using command FILLET (f). Then using commands BREAK (br) and PEDIT (pe) model such separated parts of future surface defined curves.

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20. Set an axonometric view 21. Rotate UCS around X axes:

. (X Axis Rotate UCS) in 90 degrees.

22. Prepare defining elliptical curves:  Draw a (red) line of 8 mm length. Then draw two ellipses using command ELLIPSE (el).  Trim needles parts of drawn ellipses. Use command TRIM (tr).

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Use to rotate UCS around Y axis. Draw an ellipse in another direction. Trim needles part of a drawn ellipse.

All defining curves for seat surface are already prepared. 23. Set layer SURFACE2 current and draw surface.

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Use command EDGESURF Select the curves shown in the first picture below. Draw another side of the seat surface in an analogous way.

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Make a mirror copy to create full seat surface. Use command MIRROR3D points 5, 6 and 7 to specify three points of mirror plane).

(pick

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24. Draw seat back of the chair:

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Move UCS to the endpoint of the upper vertical line. Use Draw two lines – define curves of seat back surface.

(UCS Origin).

Command: LINE Specify first point: 0,0,2 Specify next point or [Undo]: @0,-12,0 Specify next point or [Undo]: @50,0,0 Specify next point or [Close/Undo]: ↓

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Create tabulated surface Make a copy of already created surface. Use command COPY (c) (0, 0,-4).

25. Finish the drawing:

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Return UCS World . Turn off layers CURVE and AXIS. Turn on GOURAUD Shaded Shade mode to see better visual result.

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