Aptitude - How to solve cube problems, like a big cube is divided into 64 smaller cubes. Some sides are painted in blue, red or green. Guide me how to.

Contents • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Chapter 1 -- General [ ] OpenSCAD User Manual/The OpenSCAD Language. Example elements with lengths from len() e = [ [1], [], [3,4,5], 'string', 'x', [[10,11],[12,13,14],[[15,16],[17]]] ]; // length 6 address length element e[0] 1 [1] e[1] 0 [] e[5] 3 [ [10,11], [12,13,14], [[15,16],[17]] ] e[5][1] 3 [ 12, 13, 14 ] e[5][2] 2 [ [15,16], [17] ] e[5][2][0] 2 [ 15, 16 ] e[5][2][0][1] undef 16 e[3] 6 'string' e[3 ][2] 1 'r' s = [2,0,5]; a = 2; s[a] undef 5 e[s[a]] 3 [ [10,11], [12,13,14], [[15,16],[17]] ] vector operators [ ] concat [ ] [ Note: Requires version 2015.03 or later] concat() combines the elements of 2 or more vectors into a single vector. No change in nesting level is made. Vector1 = [1,2,3]; vector2 = [4]; vector3 = [5,6]; new_vector = concat(vector1, vector2, vector3); // [1,2,3,4,5,6] string_vector = concat('abc','def'); // ['abc', 'def'] one_string = str(string_vector[0],string_vector[1]); // 'abcdef' len [ ] len() is a function which returns the length of vectors or strings.

Indices of elements are from [0] to [length-1]. Vector Returns the number of elements at this level. Single values, which are not vectors, return undef. String Returns the number of characters in string. A = [1,2,3]; echo(len(a)); // 3 Matrix [ ] A matrix is a vector of vectors. Example which defines a 2D rotation matrix mr = [ [cos(angle), -sin(angle)], [sin(angle), cos(angle)] ]; Getting input [ ] Now we have variables, it would be nice to be able to get input into them instead of setting the values from code.

There are a few functions to read data from DXF files, or you can set a variable with the -D switch on the command line. Getting a point from a drawing Getting a point is useful for reading an origin point in a 2D view in a technical drawing. The function dxf_cross will read the intersection of two lines on a layer you specify and return the intersection point. This means that the point must be given with two lines in the DXF file, and not a point entity. TotalWidth = dxf_dim ( file = 'drawing.dxf', name = 'TotalWidth', layer = 'SCAD.Origin', origin =[ 0, 0 ], scale = 1 ); For a nice example of both functions, see Example009 and the image on the.

Chapter 2 -- 3D Objects [ ] OpenSCAD User Manual/The OpenSCAD Language [ ] cube [ ] Creates a cube in the first octant. When center is true, the cube is centered on the origin. Argument names are optional if given in the order shown here. Cube(size = [x,y,z], center = true/false); cube(size = x, center = true/false); parameters: size single value, cube with all sides this length 3 value array [x,y,z], cube with dimensions x, y and z. Center false (default), 1st (positive) octant, one corner at (0,0,0) true, cube is centered at (0,0,0) default values: cube(); yields: cube(size = [1, 1, 1], center = false); examples: equivalent scripts for this example cube(size = 18); cube(18); cube([18,18,18]);. Cube(18,false); cube([18,18,18],false); cube([18,18,18],center=false); cube(size = [18,18,18], center = false); cube(center = false,size = [18,18,18] ); equivalent scripts for this example cube([18,28,8],true); box=[18,28,8];cube(box,true); sphere [ ] Creates a sphere at the origin of the coordinate system.

The r argument name is optional. To use d instead of r, d must be named. Parameters r Radius.

This is the radius of the sphere. The resolution of the sphere will be based on the size of the sphere and the $fa, $fs and $fn variables. For more information on these special variables look at: d Diameter.

This is the diameter of the sphere. (NOTE: d is only available in versions later than 2014.03. Center = true equivalent scripts cylinder(h=20, r=10, center=true); cylinder( 20, 10, 10,true); cylinder( 20, d=20, center=true); cylinder( 20,r1=10, d2=20, center=true); cylinder( 20,r1=10, d2=2*10, center=true); use of $fn Larger values of $fn create smoother, more circular, surfaces at the cost of longer rendering time.

Some use medium values during development for the faster rendering, then change to a larger value for the final F6 rendering. However, use of small values can produce some interesting non circular objects. A few examples are show here: •. Scripts for these examples cylinder(20,20,20,$fn=3); cylinder(20,20,00,$fn=4); cylinder(20,20,10,$fn=4); undersized holes When using cylinder() with difference() to place holes in objects, the holes will be undersized. This is because circular paths are approximated with polygons inscribed within in a circle. The points of the polygon are on the circle, but straight lines between are inside. To have all of the hole larger than the true circle, the polygon must lie wholly outside of the circle (circumscribed).

Notes on accuracy Circle objects are approximated. The algorithm for doing this matters when you want 3d printed holes to be the right size.

Current behavior is. Discussion regarding optionally changing this behavior happening in a polyhedron [ ] A polyhedron is the most general 3D primitive solid. It can be used to create any regular or irregular shape including those with concave as well as convex features. Curved surfaces are approximated by a series of flat surfaces.

Polyhedron( points = [ [X 0, Y 0, Z 0], [X 1, Y 1, Z 1]. ], triangles = [ [P 0, P 1, P 2].

], convexity = N); // before 2014.03 polyhedron( points = [ [X 0, Y 0, Z 0], [X 1, Y 1, Z 1]. ], faces = [ [P 0, P 1, P 2, P 3.]. ], convexity = N); // 2014.03 & later Parameters points Vector of 3d points or vertices.

Each point is in turn a vector, [x,y,z], of its coordinates. Points may be defined in any order. N points are referenced, in the order defined, as 0 to N-1. Triangles (deprecated in version 2014.03, use faces) Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 points from the points vector.

Faces (introduced in version 2014.03) Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 or more points from the points vector.

Faces may be defined in any order. Define enough faces to fully enclose the solid, with no overlap. Points which describe a single face must all be on the same plane. Convexity Integer. The convexity parameter specifies the maximum number of faces a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode.

It has no effect on the polyhedron rendering. For display problems, setting it to 10 should work fine for most cases. Default values: polyhedron(); yields: polyhedron(points = undef, faces = undef, convexity = 1); All faces must have points ordered in the same direction. OpenSCAD prefers clockwise when looking at each face from outside inwards.

The back is viewed from the back, the bottom from the bottom, etc. Example 1 Using polyhedron to generate cube( [ 10, 7, 5 ] ). Unfolded cube faces CubePoints = [ [ 0, 0, 0 ], //0 [ 10, 0, 0 ], //1 [ 10, 7, 0 ], //2 [ 0, 7, 0 ], //3 [ 0, 0, 5 ], //4 [ 10, 0, 5 ], //5 [ 10, 7, 5 ], //6 [ 0, 7, 5 ]]; //7 CubeFaces = [ [0,1,2,3], // bottom [4,5,1,0], // front [7,6,5,4], // top [5,6,2,1], // right [6,7,3,2], // back [7,4,0,3]]; // left polyhedron( CubePoints, CubeFaces ); equivalent descriptions of the bottom face [0,1,2,3], [0,1,2,3,0], [1,2,3,0], [2,3,0,1], [3,0,1,2], [0,1,2],[2,3,0], // 2 triangles with no overlap [1,2,3],[3,0,1], [1,2,3],[0,1,3], Example 2 A square base pyramid. Example 1 showing only 2 faces CubeFaces = [ /* [0,1,2,3], // bottom [4,5,1,0], // front */ [7,6,5,4], // top /* [5,6,2,1], // right [6,7,3,2], // back */ [7,4,0,3]]; // left Mis-ordered faces [ ] Example 4 a more complex polyhedron with mis-ordered faces When you select 'Thrown together' from the view menu and compile the design ( not compile and render!) you will see a preview with the mis-oriented polygons highlighted. Unfortunately this highlighting is not possible in the OpenCSG preview mode because it would interfere with the way the OpenCSG preview mode is implemented. Coolorus Photoshop Download Free. ) Below you can see the code and the picture of such a problematic polyhedron, the bad polygons (faces or compositions of faces) are in pink. // Bad polyhedron polyhedron ( points = [ [ 0, - 10, 60 ], [ 0, 10, 60 ], [ 0, 10, 0 ], [ 0, - 10, 0 ], [ 60, - 10, 60 ], [ 60, 10, 60 ], [ 10, - 10, 50 ], [ 10, 10, 50 ], [ 10, 10, 30 ], [ 10, - 10, 30 ], [ 30, - 10, 50 ], [ 30, 10, 50 ] ], faces = [ [ 0, 2, 3 ], [ 0, 1, 2 ], [ 0, 4, 5 ], [ 0, 5, 1 ], [ 5, 4, 2 ], [ 2, 4, 3 ], [ 6, 8, 9 ], [ 6, 7, 8 ], [ 6, 10, 11 ], [ 6, 11, 7 ], [ 10, 8, 11 ], [ 10, 9, 8 ], [ 0, 3, 9 ], [ 9, 0, 6 ], [ 10, 6, 0 ], [ 0, 4, 10 ], [ 3, 9, 10 ], [ 3, 10, 4 ], [ 1, 7, 11 ], [ 1, 11, 5 ], [ 1, 7, 8 ], [ 1, 8, 2 ], [ 2, 8, 11 ], [ 2, 11, 5 ] ] ). Polyhedron with badly oriented polygons Succinct description of a 'Polyhedron' * Points define all of the points/vertices in the shape.

* Faces is a list of flat polygons that connect up the points/vertices. Each point, in the point list, is defined with a 3-tuple x,y,z position specification.

Points in the point list are automatically given an identifier starting at zero for use in the faces list (0,1,2,3. Each face, in the faces list, is defined by selecting 3 or more of the points (using the point identifier) out of the point list. Faces=[ [0,1,2] ] defines a triangle from the first point (points are zero referenced) to the second point and then to the third point. When looking at any face from the outside, the face must list all points in a clockwise order. Alternate Face Descriptions [ ] Before 2014.03, faces could only be described via triangles. Since 2014.03, a face description can have any number of points. The points, all in the same plane, must be listed in the proper order.

Since version???, the face vertices do not have to be planar: OpenSCAD will do its best to internally subdivide the face in triangles. Note that this may lead to different results depending on the chosen face triangulation. If a specific result is needed, the non planar face should be broken in triangular pieces by the user. An alternate (correct) face definition for example 4: faces = [ [0,3,2,1], [0,1,5,4], [2,3,4,5], // outside [6,7,8,9], [7,6,10,11], [11,10,9,8], // inside [0,4,3,0,6,9,10,6], // front [1,2,5,1,7,11,8,7] // back ] Point repetitions in a polyhedron point list [ ] The point list of the polyhedron definition may have repetitions. When two or more points have the same coordinates they are considered the same polyhedron vertex. So, the following polyhedron. Example 1: Result.

OpenSCAD font list dialog OpenSCAD includes the fonts Liberation Mono, Liberation Sans, Liberation Sans Narrow and Liberation Serif. Hence, as fonts in general differ by platform type, use of these included fonts is likely to be portable across platforms. For common/casual text usage, the specification of one of these fonts is recommended for this reason.

Liberation Sans is the default font to encourage this. In addition to the installed fonts, it's possible to add project specific font files. Supported font file formats are Fonts (*.ttf) and Fonts (*.otf). The files need to be registered with use. Use After the registration, the font will also be listed in the font list dialog, so in case logical name of a font is unknown, it can be looked up there are it was registered. Right-hand grip rule You must use parameter names due to a backward compatibility issue. Convexity If the extrusion fails for a non-trival 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a 'good' value to try).

See explanation further down. Angle [ Note: Requires version 2016.XX] Defaults to 360. Specifies the number of degrees to sweep, starting at the positive X axis. The direction of the sweep follows the, hence a negative angle will sweep clockwise. Examples [ ].

OpenSCAD - a hook translate([0,60,0]) rotate_extrude(angle=270, convexity=10) translate([40, 0]) circle(10); rotate_extrude(angle=90, convexity=10) translate([20, 0]) circle(10); translate([20,0,0]) rotate([90,0,0]) cylinder(r=10,h=80); Extruding a Polygon [ ] Extrusion can also be performed on polygons with points chosen by the user. Here is a simple polygon and its 200 step rotational extrusion. (Note it has been rotated 90 degrees to show how the rotation will look; the rotate_extrude() needs it flat).

Rotate([90,0,0]) polygon( points=[[0,0],[2,1],[1,2],[1,3],[3,4],[0,5]] ); rotate_extrude($fn=200) polygon( points=[[0,0],[2,1],[1,2],[1,3],[3,4],[0,5]] ). Cube ( 10 ); translate ([ 15, 0, 0 ]) scale ([ 0.5, 1, 2 ]) cube ( 10 ); Note: Do not use negative scale values. Negative scale values appear to work for previews, but they lead to unpredictable errors when rendering through CGAL.

Use the mirror() function instead. Resize [ ] resize() is available since OpenSCAD 2013.06. It modifies the size of the child object to match the given x,y, and z. There is a bug with shrinking in the 2013.06 release, that will be fixed in the next release. Usage Example. The text in its current form is incomplete. Scalar Arithmetical Operators [ ] The scalar arithmetical operators take numbers as operands and produce a new number.

+ add - subtract * multiply / divide% modulo The '-' can also be used as prefix operator to negate a number. Relational Operators [ ] Relational operators produce a Boolean result from two operands. = greater equal >greater than If both operands are simple numbers, the meaning is self-evident.

If both operands are strings, alphabetical sorting determines equality and order. E.g., 'ab' >'aa' >'a'. If both operands are Booleans, true >false. If one operand is Boolean, the other operand is converted to Boolean before the comparison is made.

If both operands are vectors, OpenSCAD performs an element-by-element comparison and can only result in true if the vectors are equal in size and each and every pair of elements results in true upon the comparison. Otherwise, false is returned. Vectors of different sizes are treated as unequal for '==' and '!=' operators, and always result in false for '>', '>=', ' etc.) anything result in false.

Nan doesn't equal anything. Logical Operators [ ] All logical operators take Booleans as operands and produce a Boolean.

Non-Boolean quantities are converted to Booleans before the operator is evaluated. && logical AND logical OR! Logical unary NOT Since [false] is true, false [false] is also true. Note that how logical operators deal with vectors is different than relational operators: [1, 1] >[0, 2] is false, but [false, false] && [false, false] is true. Conditional Operator [ ] The?: operator can be used to conditionally evaluate one or another expression. It works like the?: operator from the family of C-like programming languages.?: Conditional operator Usage Example. The text in its current form is incomplete.

Trigonometric Functions [ ] The trig functions use the C Language mathematics functions, which are based in turn on Binary Floating Point mathematics, which use approximations of Real Numbers during calculation. OpenSCAD's math functions use the C++ 'double' type, inside Value.h/Value.cc, A good resource for the specifics of the C library math functions, such as valid inputs/output ranges, can be found at the Open Group website & cos [ ] Mathematical cosine function of degrees. See Parameters Decimal.

Angle in degrees. Usage Example. The text in its current form is incomplete. Str [ ] Convert all arguments to strings and concatenate. Usage examples: number=2; echo ('This is ',number,3,' and that's it.'

); echo (str('This is ',number,3,' and that's it.' )); Results: ECHO: 'This is ', 2, 3, ' and that's it.' ECHO: 'This is 23 and that's it.' Chr [ ] [ Note: Requires version 2015.03] Convert numbers to a string containing character with the corresponding code.

OpenSCAD uses Unicode, so the number is interpreted as Unicode code point. Numbers outside the valid code point range will produce an empty string. Parameters chr(Number) Convert one code point to a string of length 1 (number of bytes depending on UTF-8 encoding) if the code point is valid. Chr(Vector) Convert all code points given in the argument vector to a string. Chr(Range) Convert all code points produced by the range argument to a string. The text in its current form is incomplete. [ Note: Requires version 2015.03] Basic Syntax [ ] The list comprehensions provide a flexible way to generate lists using the general syntax [ list-definition expression ] The following elements are supported to construct the list definition for (i = sequence) Iteration over a range or an existing list if (condition) Selection criteria, when true the expression will be calculated and added to the result list let (x = value) Local variable assignment for [ ] The for element defines the input values for the list generation, the syntax is the same as used by the iterator.

[ for (i = [start: step: end]) i ] Generate output based on a range definition, this version is mainly useful to calculate list values or access existing lists using the range value as index. // calculate Fibonacci numbers function func ( x ) = x. // input: list of numbers // output: sorted list of numbers function quicksort ( arr ) =! ( len ( arr ) >0 )? []: let ( pivot = arr [ floor ( len ( arr ) / 2 )], lesser = [ for ( y = arr ) if ( y pivot ) y ] ) concat ( quicksort ( lesser ), equal, quicksort ( greater ) ); // use seed in rands() to get reproducible results unsorted = [ for ( a = rands ( 0, 10, 6, 3 )) ceil ( a )]; echo ( unsorted ); // ECHO: [6, 1, 8, 9, 3, 2] echo ( quicksort ( unsorted )); // ECHO: [1, 2, 3, 6, 8, 9] Selecting elements of a vector [ ] select() performs selection and reordering of elements into a new vector.

Function select ( vector, indices ) = [ for ( index = indices ) vector [ index ] ]; vector1 = [[ 0, 0 ],[ 1, 1 ],[ 2, 2 ],[ 3, 3 ],[ 4, 4 ]]; selector1 = [ 4, 0, 3 ]; vector2 = select ( vector1, selector1 ); // [[4, 4], [0, 0], [3, 3]] vector3 = select ( vector1,[ 0, 2, 4, 4, 2, 0 ]); // [[0, 0], [2, 2], [4, 4],[4, 4], [2, 2], [0, 0]] // range also works as indices vector4 = select ( vector1, [ 4:- 1: 0 ]); // [[4, 4], [3, 3], [2, 2], [1, 1], [0, 0]] Concatenating two vectors [ ] Using indices. Compiling design (CSG Tree generation).

ERROR: Assertion 'false' failed, line 2 Compiling design (CSG Products generation). Geometries in cache: 0 Geometry cache size in bytes: 0 CGAL Polyhedrons in cache: 0 CGAL cache size in bytes: 0 Compiling design (CSG Products normalization). Normalized CSG tree has 0 elements Compile and preview finished. Total rendering time: 0 hours, 0 minutes, 0 seconds This example has little use, but the simple assert(false); has. Hum Sath Sath Hain Full Movie Download Kickass. Assert(false); can be used in code sections that should be unreachable. Checking parameters [ ] A useful example is checking the validity of input parameters. //example 1 function func0 () = 5; function func1 ( x = 3 ) = 2 * x + 1; function func2 () = [ 1, 2, 3, 4 ]; function func3 ( y = 7 ) = ( y == 7 )?

5: 2; function func4 ( p0, p1, p2, p3 ) = [ p0, p1, p2, p3 ]; echo ( func0 ()); // 5 a = func1 (); // 7 b = func1 ( 5 ); // 11 echo ( func2 ()); // [1, 2, 3, 4] echo ( func3 ( 2 ), func3 ()); // 2, 5 z = func4 ( func0 (), func1 (), func2 (), func3 ()); // [5, 7, [1, 2, 3, 4], 5] translate ([ 0, - 4 * func0 (), 0 ]) cube ([ func0 (), 2 * func0 (), func0 ()]); // same as translate([0,-20,0])cube([5,10,5]). // recursion example: add all integers up to n function add_up_to ( n ) = ( n == 0? 0: n + add_up_to ( n - 1 ) ); There is a built-in recursion limit to prevent an application crash (a few thousands). If the limit is hit, you get an error like: ERROR: Recursion detected calling function..

For some special cases of functions, OpenSCAD is able to eliminate internally the recursion transforming it in an iterative loop. The special forms are: function recurse(.) =?: recurse(.); and function recurse(.) =? Recurse(.):; The previous example code does not match any of these forms.

But the following is entitled to tail-recursion elimination. The text in its current form is incomplete. Modifier characters are used to change the appearance or behaviours of child nodes.

They are particularly useful in debugging where they can be used to highlight specific objects, or include or exclude them from rendering. Advanced concept [ ] As OpenSCAD uses different libraries to implement capabilities this can introduce some inconsistencies to the F5 preview behaviour of transformations. Traditional transforms (translate, rotate, scale, mirror & multimatrix) are performed using OpenGL in preview, while other more advanced transforms, such as resize, perform a CGAL operation, behaving like a CSG operation affecting the underlying object, not just transforming it. In particular this can affect the display of modifier characters, specifically '#' and '%', where the highlight may not display intuitively, such as highlighting the pre-resized object, but highlighting the post-scaled object. Note: The color changes triggered by character modifiers will only be shown in 'Compile' mode not 'Compile and Render (CGAL)' mode. (.) Background Modifier [ ] Ignore this subtree for the normal rendering process and draw it in transparent gray (all transformations are still applied to the nodes in this tree).

Because the marked subtree is completely ignored, it might have unexpected effects in case it's used, for example, with the first object in a difference(). In that case this object will be rendered in transparent gray, but it will not be the base for the difference()!