SUBDIVISION SURFACE Modelling IN BLENDER PART 16 | The Bishop The Bishop The bishop is the one that most people get really wrong. Fair enough. It is a complicated shape and polygon modelling techniques will get you nowhere near it. The notch cut into the head of the bishop is the problem and the solution most people choose is using a boolean modifier of some sort. This will get you a shape which looks like a bishop but the model you have will be really difficult to work with, the subdivision modifier will not be able to smooth it and the it will render terribly. It could be retopologised by hand but that is a lengthy and difficult prospect. Better to consider creating it as a subdivision surface from the outset and that means thinking about the flow of topology around the shape. Boolean operations care nothing for flow so they are useless to us here. This brings us back to our problem. And the solution is edge flow. Think about applying small squares over one of the curves that make up the edge of the cut on a bishop and you will find yourself wanting to lay them end to end along the curve. This means that that particular area of the model has a flow. It is too difficult to place these things by hand so we need to think about the nature of the shape of the head. It is vaguely spherical so we can think about starting with a sphere. The UV sphere is no good to us as it has limited flow in too many directions. We like working in quads so maybe the quad sphere can help us. It has lots of good flow that we can redirect over those curves. This makes it sound complicated. It’s not really. The best way to demonstrate it, as with all modelling problems, is to start doing it. So let’s go. 01 | Creating the Head After looking through my reference photographs I decided that this one was the one I was going to vaguely follow. Press ‘Ctrl-n’ and start a new ’general’ scene in blender. Immediately press ‘Ctrl-Shift-s’ to save this scene somewhere sensible within your project. Call it “Bishop” Change to the front view by pressing ‘1’ on the numberline and add your reference image using the same method we used in the Pawn chapter and rename it “bishop reference image” The Bishop 16.1 Creating the head 16.2 Matching the reference We can use the default cube to create our initial quadsphere so with the ‘cube’ selected , press ‘f2’ to rename it to “bishop” Press ‘Crtl-3’ to add a subdivision surface modifier with three levels of subdivision. You can do it with 2 subdivision levels for a lighter mesh (less than 500 faces in total when complete) with excellent results. A subdivision of level 4 makes for a slightly wider cut in the final bishop than I want. Other subdivision levels are actually available between these numbers but that is a more advanced technique which I will leave alone for this discussion. level 1 subdivision requires even more advanced techniques that I won’t go into here but does result in a great bishop with less than 100 faces! I will show some examples of these at the end of this section. Apply the subdivision surface modifier immediately. ( press ‘ctrl-a’ while hovering the mouse cursor over its property editor in the modifier property stack. Now ‘Tab’ to edit mode and press ‘Ctrl-alt-s’ and drag the mouse cursor all the way to the right to turn our bishop into a sphere. Now ‘Tab’ back to object mode and add a subdivision surface modifier to the ‘bishop’ by pressing ‘Ctrl- 3’ . Set the shading to smooth by ‘right clicking’ and selecting ‘smooth’ from the pop up menu. Now move the ‘bishop’ object up in (Z) by pressing ‘g’ to translate it up with the mouse. Now press ‘s’ to scale it down to approximate the size and position of the bishop in your reference image. Click the ‘ eye icon’ beside the ‘bishop reference image’ to hide it for now. We need to change the shape of our bishop but we will be working with unusual topology so it is best that we use another copy of this sphere as a target shape to wrap our Bishop around. Make a copy of our Bishop by pressing ‘Shift-d’ then immediately ‘right click’ to leave it in place. Press ‘f2’ to rename this new object ‘bishop target’ Hide this object for the moment by clicking the ‘eye icon’ by it’s name in the outliner and reslect our ‘bishop’ object. The Bishop 16.3 Selecting the center faces Inset faces properties Press ‘1’ and then ‘.’ on the numpad to switch to the front view and fill the 3d viewport with our model. A lot of what we will do relies very heavily on the view we are working in so pay close attention to your view at all times. Press ‘Shift-z’ to use wireframe mode . We need to make sure the faces on all sides of the model are selectable and this is the easiest way to achieve this. ‘Tab’ into edit mode and press ‘3’ on the number line to make sure you are in face select mode Press ‘alt-a’ to deselect all of the vertices then press ‘b’ to box select the middle 2 columns of faces from the top of the mesh to somewhere past the halfway mark (just drag the mouse over them creating a selection!). It doesn’t really matter how many rows you select but just past the halfway mark is good for now. Once you know the technique you can easily decide how deep you want the cut to be. Now press ‘i’ to inset these faces and move the mouse a little to activate the inset operation. Don’t worry about placing the inset anywhere in particular; we will decide where it goes in the properties box which appears (in the bottom left of the 3d view) after you ‘left-click’ to confirm the inset operation. In the ‘inset faces’ property box , check the ‘Offset Relative’ tick box and change the ‘Thickness’ to “0.5” You can now press ‘x’ and select ‘delete faces’ to cut a hole in our mesh which leaves an entire closed loop of faces flowing around its edge. This is the main practical use of the inset tool; to create new boundaries and areas of flow around features of a model. It is often just thought of as an Extrusion then a Scale but, while this is effectively what is happening, it’s use should be thought of completely seperately from Extrude. It is used to create new areas of flow. Press ‘Shift-z’ again to switch to solid shading mode and have a look around our bishop so far. While our topology is good, it is not yet very bishopy(!) We want to change its overall shape and rather than pulling points around by hand on our neat mesh (and likely breaking it by doing so) we can shape the bishop using another mesh. Sounds complicated again, but it really is not! ‘Tab’ back to object mode and click the ‘eye icon’ beside our ‘bishop’ in the outliner to turn off it’s visibility. Select the ‘eye icon’ beside our ‘bishop target’ object to display it then select it. We can now work on the overall shape of the bishop’s head. ‘Tab’ into edit mode and make sure you are in the front view ( press ‘1’ on the numpad ) and in vertex selection mode (“1” on the main number line). At the top middle of the 3d view there are some controls for ‘ proportional editing’ . This just means that a circle of influence around anything you select is used to proportionally move surrounding points. Best just to demonstrate it! From the ‘ circular menu button’ at the top of the 3d view select ‘sharp’ and make sure the small circle next to it is blue (you can press ‘o’ to toggle proportional editing on and off.) Move the mouse pointer to just above the very center of the mesh and ‘left click’ to select the topmost vertex. Now press ‘g’ to start translating this vertex and press ‘z’ to constrain the movement to the vertical (Z axis). Cutting out the notch 16.4 deleted faces the initial shape proportional editing: Sharp You will notice a circle around the point you have selected which shows the circle of influence for the proportional editing tool. Scrolling the mouse wheel will change the size of this circle to encompass more or less surrounding points. I made the circle slightly larger than half of the mesh and moved the point up.once you are happy with the shape, press ‘Tab’ to go back to object mode and add a subdivision surface modifier to the object by pressing ‘Ctrl-3’ I have very quickly make a bishop shape from this mesh by manipulating just one vertex but when you know more about some of the available tools in blender you will be able to shape objects in much more interesting ways. lattices, which we cover when we make the queen and the rook modelling sections, will be a great help for this. You can now press ‘h’ to hide this object. We dont need to be able to see it while we are working. ( pressing ‘h’ is the same as clicking the ‘eye icon’ beside it’s name in the outliner !) Now click the ‘eye icon’ next to our ‘bishop’ object in the outliner so we can see it again and select it. In the modifiers panel click the ‘Add Modifier’ drop down menu and select ‘Shrinkwrap’ from the pop up menu. Move this modifier to the top of the stack (below the subdivision surface modifier) by either dragging it up using the 8 small dots in the top right hand corner of the modifier or by selecting ‘move to first’ from the drop down menu in the modifier. Shrinkwrap is a very powerful modifier capable of many excellent results and is perfect for our needs here. The Bishop 16.5 Proportional editing of the target shape Shrinkwrap on top Select our ‘bishop target mesh’ in the outliner or in the 3d view after pressing the ‘eyedropper’ next to ‘Target’ We want to set the ‘Wrap Method’ to ‘Project’ This offers a very precise method of projecting the vertices of our model onto the target shape. Enable the ‘Negative’ check box . With both the Positive and Negative checkboxes enabled, the modifier will do its best to find a way to move every point on our ‘bishop’ towards the target mesh. Increase the ‘Subdivision Levels’ to “2” Finally, click the ‘on cage’ button at the top of the modifier so that we can work on our shape in edit mode and see the results immediately. Now is a good time to add a subidivison surface modifier to our ‘bishop’ with ‘ctrl-3’ and set our object shading to smooth shading (by ‘right clicking’ in the 3d view and selecting ‘Shade Smooth’ in the pop up menu.) Before proceeding, make sure that proportional editing is turned off. ( press ‘o’ until the circle at the top of the 3d view is greyed out.) You can press ‘h’ with the ‘bishop target shape’ selected to hide it. The modifier will still use it while it is hidden and this keeps it out of our way while we work. Switch the transform pivot to ‘Active element’ using the menu at the top of the 3d view to use the objects center as our transformation pivot. Still in object mode, press ‘1’ on the numpad to make sure you are in the front view and press ‘r’ to rotate our mesh with the mouse. As it rotates it will do its best to adhere to the shape of our ‘target bishop’ allowing us to correctly angle our cutout. Shaping the head 16.6 Shrinkwrap modifier properties rotating while shrinkwrapped It will make life a little easier later on if one of the points of our mesh is more or less aligned with the very top point of the shape but it does not matter too much. This can be achieved by rotating the mesh in wireframe mode rather than solid view (toggled with “Shift-Z”). If you want the angle of your cutout to match your reference shot, prioritize that. The edges of our cutout curl out a little and that is not what we want. Accidental “features” like this can be just what you want but you should also have the skills to get rid of them if you can. You can always put them back in a more considered way later on if you want. We will straighten these cuts in edit mode and you will now need to become a little more comfortable rotating around your mesh with the ‘middle mouse’ and ‘shift-middle mouse’ controls. Regularly pressing ‘.’ on the numpad to frame objects and selections in the 3d view should become second nature by the end of this exercise! Press ‘Tab’ to switch to edit mode and make sure you are in vertex selection mode by pressing ‘1’ on the numberline Firstly, select two opposing corner vertices at the bottom of the cut by ‘left-clicking’ one of them then ‘shift- left-clicking’ the other. Press ‘shift-s’ and select ‘cursor to selected’ to move the 3D-cursor directly between these two points. Now ‘Shift’ (or ‘ctrl’ ) select all of the other vertices between these two points around this side of the cut. Holding ‘ctrl’ when clicking points asks blender to find the shortest route to a point from the last vertex you selected, Then it selects all of the points between. It may not select the points you hope for so move short distances until you feel you know how it works. Make sure all the vertices around one side of the cut are selected from corner to corner. The Bishop 16.7 Selecting Corner Vertices Make sure the transform pivot point (in the menu at the top of the 3D view ) is set to ‘3D Cursor’ In the ‘N-panel’ ( press ‘n’ to toggle it on and off), select the ‘ edit’ tab and from the ‘loop tools’ menu, press ‘Flatten’ If required these vertices can be rotated while you are in the front view by pressing ‘1’ on the numberline (they will all obey the 3d-cursor rotation center and the shrinkwrap modifier so our shape will remain close to the shape we want. You should now repeat these steps for the other side of the cut ( select the two corner vertices , move the 3d cursor between them, select the rest of the vertices between them , ‘Flatten’ the using ‘loop tools’ and rotate in the front view if required.) We now want to add the loop which will mark the begining of our curvature over the lip of the cut while the shape is still under the control of the shrinkwrap modifier. Press ‘Ctrl-r’ and add a loop between the first faces et the edge of the cut. it will encircle the cut creating an entire closed loop. We can now ‘left click’ to confirm this loop which puts blender into Loop Slide mode (the same as if you had selected the loop and pressed ‘gg’ .) While this mode is active, you can press ‘e’ to force the edges which make up this loop to be equally distanced from one of the edges surrounding it. Pressing ‘e’ now and ‘left clicking’ to confirm, will make sure that the curvature over the edge of the cut (which we can’t see yet!) will be even all the way around. Shaping the head 16.8 Entire edge selected Loop Tools: Flatten New loop around the shell Before we finish modelling the cut, we want to take further advantage of the shrinkwrap modifier which is trying it’s best to hold our shape. We will cut a hole in the bottom of the head which we can use later to extrude the body; just as we did with the ‘pawn’ In edit mode and again in the front view ( ‘1’ on the numpad ), click just below the middle bottom vertex of the mesh. This will select that vertex. You can now press ‘Ctrl-+’ once to grow this selection. Now hit ‘x’ and select ‘vertices’ to leave a hole in our model. orbit the camera around so you can clearly see this hole and ‘Alt-click’ one of the edges which makes up the loop around the hole to select the whole loop. Make sure that the transform pivot is set to ‘median point’ for the next part. We almost always use ‘median point’ when extruding new geometry (which we are about to do!) Press ‘e’ to extrude and then immediately press ‘s’ to scale. Moving the mouse, you will see a new loop which can be scaled down to create a new ring of faces inside the hole. As with the pawn, this edge will try to flow over the surface being as it is being controlled by the shrinkwrap modifier. Scale this loop so that it seems an appropriate distance; keeping the new faces approximately the same size as everything surronding it. ‘Left click’ to confirm the position of the new loop. As with the ‘pawn’ , we want to transition to a circular hole and this loop will be the first step. In the ‘N-panel’ click the ‘circle’ function inside ‘loop tools’ The Bishop 16.9 Bottom Vertex selected Bottom vertices deleted recontructed hole In the ‘temporary property editor’ for the circle operation (found at the bottom left hand corner of the 3d-view ), set the ‘influence’ to “50%” Now we can press ‘e’ to extrude again and immediately press ‘s’ to scale it down yet again. Move it a reasonable distance and ‘left click’ again to confirm its position. Hit the ‘circle’ button again in the ‘N-panel’ but this time set the ‘influence’ to “100%” Finally, extrude and slightly scale down one final loop. (This one defines the curvature which will flow into the body and can be a smaller move.) You can now ‘Tab’ back to object mode and look at the mesh to make sure that everything is smooth. 01 | Filling in the gaps We are finished with the shrinkwrap modifier and it must now be applied by pressing ‘ctrl-a’ while hovering the mouse cursor over its ‘property editor’ in the modifier stack. If the shrinkwrap modifier is not applied at this stage we would not be able to fill in the cuts as any new geometry would be forced to follow the shape of our ‘target bishop’ We are finished with the ‘bishop target shape’ object now and it can be deleted Select it in the outliner and press ‘del’ Press ‘Tab’ to switch to edit mode and change the transform pivot back to ‘3D-cursor’ (using the menu at the top middle of the 3d view ). It is now time to fill in the mesh but we will do it with a view to maintaining precise edge flow by making sure faces are correctly proportioned and we have just the right amount of them. In order for the curvature over the edge of our cut to be consistant all the way around, the faces which surround it should all be the same width from the edge. We have already created a loop on the outershell to make sure the curvature flowing into the curve is consistant but now we need to do something similar on the inside of the ‘notch’ on our bishop. As we did in an earlier previous step, we need to select two opposing corner vertices at the bottom of the cuts and move the 3d-cursor between them. ( Select one of the vertices then ‘shift-select’ the other. Finally, press ‘Shift-s’ and select ‘Cursor to selected’ from the radial menu which appears.) Finishing the shrinkwrap 16.10 Again, select all of the vertices between these two points along the edge of the cut. Using either ‘Shift’ or ‘Ctrl’ while clicking the points between our two corner vertices. (Using ‘Ctrl’ is quicker once you become used to it!) Now press ‘e’ to extrude and immediately press ‘s’ to scale them and type “0.7” before hitting ‘Enter’ . This extrudes the edges down toward the 3d cursor which will give us our first of of the internal faces we need. Repeat these steps for the other side of the cut ( Move the 3d cursor between the two corner vertices , Select the rest of the vertices which make up this side of the cut, press ‘e’ to extrude and scale by “0.7” ) We can now make use of the excellent ‘f2’ add-on (It works in the background but without it enabled, the next tasks can be a real pain.) The ‘f2’ addon calculates where a new face should go when the ‘f’ key is pressed in edit mode If a single vertex is selected, the add-on will attempt to create a new vertex based on the position of two other connected and exposed vertices (meaning - not surrounded completely by faces). It will always create an extra vertex even if it seems more logical to use an exisitng vertex. If an edge is selected, the ‘f2’ add-on will expect two other connected, exposed edges to either create a fourth edge which it can then fill in as a face. If a face can be create using four existing enclosed edges, the “f2” addon will use these four edges to create the face do this instead of creating a new edge. The Bishop 16.11 3d-cursor moved between corners All vertices on one edge selected Edges extruded and scaled by 0.7 If more than two edges are selected the ‘f2 add-on will connect them with two new edges and fill in the resulting viable face. If two adjacent edges are selected it will create a triangle which we would normally like to avoid. With more than two edges selected it will create an n-gon which we never want! Select one of the internal corner vertices at the bottom of the cut and press ‘f’ . The ‘f2’ addon lets blender know to create a new vertex and a filled face based on two other surrounding exposed (meaning not fully surrounded by faces) points. ‘Right-click’ immediately to cancel any movement and one of our faces will be created correctly. The other face cannot be filled in using this method as it would create a floating vertex rather than connecting the existing ones. Instead, switch to edge select mode by pressing “2” on the numberline and select the exposed edge of our shell before pressing “f” . The ‘f2’ addon will correctly use the surrounding edges to create a new edge and a filled face. Filling in the cut 16.12 Select corner vertex press “f” then right click select the exposed edge Press “f” then right click Now move the camera to the other side of the model and repeat this process for the four missing faces on the other side of the cut. You may have noticed that the curve of the surface over the top of the model is much looser than the curve at the corners of the cut. This is beacause our faces are different widths from the edge and not what we want so let’s fix that next. It is an easy fix in blender. Press ‘Ctrl-r’ (to add a loop cut) and position the mouse cursor so that the yellow loop guide appears around the entire new inside edge of the cut. “Left-click” to confirm this loop which puts blender into loop slide mode . Now press ‘e’ and blender will calculate a new position for the edges which make up the loop which makes them an equal distance from each point along the edge. (you will see a small red dot on one of the edges it is using to calculate the distance) ‘left click’ to finalise this loop. Our curvature over the edge is now consistent around the whole profile. With this loop selected , use the ‘mark seam’ option from the ‘Right click’ menu to make it red. This is the loop which will control the curvature over the lip of the cut. Add one more loop cut ( ‘Ctrl-r’ ) around the bigger polygons inside the mesh. Anywhere will do but again press “e” to make the loop evenly spaced from the edge of our control loop. This is the holding loop for our curve and will not be moved. Switch to face select mode ( press ‘3’ on the numberline ) and “Alt-click” any of the internal edges to select the whole ring of faces around the inside of the mesh. Press ‘x’ and select ‘delete faces’ from the pop up menu. The Bishop 16.13 Add a loop, left click, press “E” A second evenly spaced loop delete the remaining faces Our marked loop can now be used (by pressing ‘gg’ while it is selected ) to control the tightness of the curvature over the cut. As with all things in subdivision surface modelling we prefer to contol curvature rather than model it. Let’s fill in the rest of the shape (with help of the ‘f2’ add-on again.) Selecting the edges in the next steps may be easier if the ‘edit mode’ switch in the subdivision surface modifier is turned off. It can make selecting edges a little easier without the influence of the modifier showing in the 3d-view. Press ‘2’ to change to edge select mode and select two opposing edges along the inside, bottom of the shape. Press “f ” to have the ‘f2’ add on fill in this polygon. This links both sides of our cut with a single face. Filling in the cut 16.14 Turn off edit mode Select two opposing edges Press “F” to fill in A face Now select one of the exposed edges of this new polygon and keep pressing ‘f’ until all of faces on that side of the mesh are filled in. You may have noticed that the very last face to get filled in is a small triangle. We can’t have that! We will deal with that in a moment. Repeat this process on the other side by selecting the other exposed edge of the polygon and pressing ‘f’ repeatedly to fill it all in. Another triangle! Press ‘Ctrl-r’ to add a loop cut and put it right in the centre of the cut. ‘left-click’ to place this loop. Triangles gone! They were at the end of each side of this loop and have, as a result, been turned into quads. This extra loop will also turn out to be handy later if we want to shape the inside of the cut. That is the main body of the head(!) done. We can now add the dibble(!!) at the top and extrude out the body employing the same methods we used to make the body of the ‘pawn’ The Bishop 16.15 Select one of the exposed edges Press “F” until all faces are filled Add a loop cut inside the shape Firstly, we will extrude some loops to make the small shape at the top of the head and as usual when we are extruding loops, we will use ‘median point’ as the transofrmation pivot point so select that now from the drop down menu found at the top middle of the 3d-view Select the very top vertex of the model (in point select mode - ‘1’ on the numberline ) and press ‘x’ to delete it ( select ‘vertices’ in the pop up menu.) This leaves a convenient hole with an even more convenient loop surrounding it which we can use to extrude ourselves a dibble. Select the loop around the new hole in our mesh and press ‘e’ to extrude then immediately press “s” to scale it down a small amount. We can use the ‘circle’ function from the ‘N-panel’ again. This time use the full influence of 100% in the temporary properties box which appears. Now move ( press ‘g’ then ‘z’ ) this circular loop up a little in (Z) Extrude another loop up in (Z) and this time press ‘s’ , ‘z’ and ‘0’ before hitting ‘enter’ to scale it in (Z) which will make it completely flat. This is necessary as it is likely at a slight angle. Creating the top 16.16 transformation pivot: median point Select and delete top vertex Looptools-circle Scale in “Z” to zero. Extrude up 2 or 3 more loops to create the shape you need at the top of the bishop. Scaling and moving the loops in (Z) as necessary. For the very top of the “dibble” select ‘grid fill’ from the ‘mesh menu’ . If it appears that two sets of parallel lines are connected across the top, simply change the ‘span’ property in the grid fill properties box (in the bottom left of the 3d-view ) until it forms a cross in the middle. You can perhaps select the very center vertex of this cross and move it up in (Z) a small amount to round off the shape. Now that the head is complete, we can move to the bottom of the mesh and start extruding. Moving the new loops in Z and scaling them to describe the body of our bishop using exactly the same techniques that we used for the pawn. It is useful to follow your reference image for this but Don’t worry about following it too closely. It is just a reference! ‘Tab’ back to object mode ‘Click’ the ‘eye icon’ beside your ‘bishop reference image’ object in the outliner to display it. It will only be visible when you are in the front- view. The Bishop 16.17 Grid fill to create the top Finished Head Extrude twice to create the top ‘Tab’ back to edit mode and orbit the camera around to the bottom and ‘Alt-click’ any of the edges around the hole to select the loop. Press ‘1’ on the numpad to switch back to the front view where your reference image can be seen and start extruding , moving an scaling loops until you have matched the shape of the body of your bishop. After your very first extrusion, scale the loop in Z to 0 ( press ‘s’ , ‘z’ , ‘0’ and hit ‘enter’ ) as it is unlikely to be completely flat at first because of our earlier modelling tasks. I will leave the you to extrude the body of your bishop as the instructions are exactly the same as the steps we used to create the ‘pawn’ in the previous lesson. I roughly followed my ‘bishop reference image’ but changed the shape towards the base to more closely match the sytle of the ‘pawn’. Continue extruding the shape of the bishop until you get to the bottom, where the last two loops you extrude should be scaled down a little without translating them. This creates a small lip for the base which we can fill in as we did with the pawn, with a ‘grid fill’ , not forgetting to ‘offset’ them in the temporary dialogue box to thve correct orientation. extruding the body 16.18 Select the loop around the hole Grid fill to close the shape Our bishop is finished. Change to one of the matcaps to have a good look around ntil you are satisfied with the result. We have good edge loops to control the curvature around the cut and all over the body. It will tolerate any subdivision, it is made from all quads, the poles have been moved to areas of minimum distortion and we are done with the modelling. As before it is now time to move the center of the geometry to the bottom of the model and make sure it is set to appropriate world scale as we did with the pawn. This file can then be saved and is ready to be imported into any scene. We can now move on to our next chess piece: The Rook. Another one that is almost always approached incorrectly. The Finished Bishop 16.19 Finished Bishop Model