METHOD AND 3D PRINTING APPARATUS FOR PRODUCTION OF A LUMINAIRE, AND A LUMINAIRE

Abstract

A method for determining a production of a luminaire (100) via 3D-printing, and a 3D-printing apparatus for production of a luminaire, and a luminaire, are provided. The method comprises the steps of defining a suspension point (110) of the luminaire, defining a fixation line (120) through the luminaire, defining a plurality of cross-sectional shapes (130) of the luminaire along the vertical axis, z, and for each cross-sectional shape of the plurality of cross-sectional shapes of the luminaire, minimizing a distance, R0, between the fixation point and a center of mass, Mt, of a first sector, S.sub.1, and a second sector, S.sub.2, of the cross-sectional shape.

Claims

1. A method for determining a production of a luminaire via 3D-printing, wherein the luminaire is intended for vertical suspension, the method comprising the steps of defining a suspension point, of the luminaire, the suspension point being an exterior point of the luminaire by which the luminaire is intended to be vertically suspended, defining a fixation line through the luminaire, the fixation line elongating from the suspension point and being parallel to a vertical axis, z, defining a plurality of cross-sectional shapes of the luminaire along the vertical axis, z, wherein each cross-sectional shape of the plurality of cross-sectional shapes extends in a plane, P, perpendicular to the vertical axis, z, and corresponds to a 3D-printing layer of the luminaire, and for each cross-sectional shape of the plurality of cross-sectional shapes of the luminaire: a) defining a fixation point as the intersection of the fixation line with the cross-sectional shape, b) defining a mass balance line in the plane, P, wherein the mass balance line intersects the fixation point, c) defining a first side and a second side of the cross-sectional shape with respect to the mass balance line, respectively, wherein the first side and the second side are arranged opposite to each other with respect to the mass balance line, d) defining a sector angle, dϕ=180°/n, wherein n is an integer, wherein for each angle ϕ=k.Math.dϕ, wherein k=1, . . . , n e) determining an extrusion of 3D-printing material of the cross-sectional shape as a function of a first sector, S.sub.1, of the sector angle, dϕ, at the angle, ϕ, in the first side, wherein the first sector, S.sub.1, is associated with a first mass, m.sub.1, of extruded 3D-printing material, and a second sector, S.sub.2, of the sector angle, dϕ, at the angle ϕ+180°, in the second side, wherein the second sector, S.sub.2, is associated with a second mass, m.sub.2, of extruded 3D-printing material, for minimizing a distance, R.sub.0, between the fixation point and a center of mass, M.sub.t, of the first sector, S.sub.1, and the second sector, S.sub.2, and in case the distance, R.sub.0, exceeds a predetermined threshold distance, R.sub.t, f) defining a connection line in the plane, P, intersecting the center of mass, M.sub.t, and the fixation point, wherein, in case the center of mass, M.sub.t, is located in the first side, determining an additional extrusion of 3D-printing material of the cross-sectional shape in the second side such that a first center of mass, M.sub.S1, of the determined additional extrusion of 3D-printing material of the cross-sectional shape of the second side coincides with the connection line in the second side and is located at a first distance, R.sub.S1, from the fixation point, for minimizing |M.sub.S1.Math.R.sub.S1−M.sub.t.Math.R.sub.0|, and wherein, in case the center of mass, M.sub.t, is located in the second side, determining an additional extrusion of 3D-printing material of the cross-sectional shape in the first side such that a second center of mass, M.sub.S2, of the determined additional extrusion of 3D-printing material of the cross-sectional shape of the first side coincides with the connection line in the first side and is located at a second distance, R.sub.S2, from the fixation point, for minimizing |M.sub.S2-R.sub.S2-M.sub.t-R.sub.0|.

2. The method according to claim 1, wherein the determining of an extrusion of 3D-printing material is based on a track width, tw, of extruded 3D-printing material perpendicular to a direction of extrusion of the 3D-printing material.

3. The method according to claim 1, wherein the luminaire is intended to be at least partially hollow, and, in at least one cross-sectional shape of the plurality of cross-sectional shapes, is intended to comprise at least one layer of 3D-printing material in a radial direction of the cross-sectional shape.

4. The method according to claim 3, wherein the luminaire, in at least one cross-sectional shape of the plurality of cross-sectional shapes, is intended to comprise a single track of 3D-printing material.

5. The method according to claim 4, wherein the step of determining the extrusion of 3D-printing material comprises, based on an intended extrusion of 3D-printing material along a first chord length, Δl.sub.1, of the first sector, S.sub.1, with a first track width, tw.sub.1, of the 3D-printing material, and along a second chord length, Δl.sub.2, of the second sector, S.sub.2, with a second track width, tw.sub.2, of the 3D-printing material, determining a first ratio, R.sub.1, between the first track width, tw.sub.1, and the second track width, tw.sub.2, such that R.sub.1=(ρ.sub.2.Math.Δl.sub.2.Math.r.sub.2)/(ρ.sub.1.Math.Δl.sub.1.Math.r.sub.1) is fulfilled, wherein r.sub.1 is the sector radius of the first sector, S.sub.1, r.sub.2 is the sector radius of the second sector, S.sub.2, ρ.sub.1 is the density of 3D-printed material along the first chord length, Δl.sub.1, and ρ.sub.2 is the density of 3D-printed material along the second chord length, Δl.sub.2.

6. The method according to claim 3, wherein the luminaire, in at least one cross-sectional shape of the plurality of cross-sectional shapes, is intended to comprise a plurality of tracks of 3D-printing material.

7. The method according to claim 6, wherein the step of determining the extrusion of 3D-printing material comprises, based on an intended extrusion of 3D-printing material along a plurality of first chord lengths, Δl.sub.1i, of the first sector, S.sub.1, wherein the plurality of first chord lengths, Δl.sub.1i, comprises an innermost first chord length, Δl.sub.11, and an outermost first chord length, Δl.sub.1n, with respect to a first sector radius, r.sub.1, of the first sector, S.sub.1, and along a plurality of second chord lengths, Δl.sub.2i, of the second sector, S.sub.2, wherein the plurality of second chord lengths, Δl.sub.2i, comprises an innermost second chord length, Δl.sub.21, and an outermost second chord length, Δl.sub.2n, with respect to a second sector radius, r.sub.2, of the second sector, S.sub.2, determining a second ratio, R.sub.2, between a first density, ρ1, of the first sector S.sub.1, and a second density, ρ.sub.2, of the second sector S.sub.2, such that R.sub.2=(Δl.sub.2n.Math.r.sub.2.Math.Δr.sub.2)/(Δl.sub.1n.Math.r.sub.1c.Math.Δr.sub.1) is fulfilled, wherein Δr.sub.1 is the radius length between a center point of the innermost first chord length, Δl.sub.11, and the outermost first chord length, Δl.sub.1n, Δr.sub.2 is the radius length between a center point of the innermost second chord length, Δl.sub.21, and the outermost second chord length, Δl.sub.2n, r.sub.1c is the radius from the fixation point to a first center point, C.sub.r1, of a first area, A.sub.1, defined by Δl.sub.1n and Δ.sub.r1, and r.sub.2c is the radius from the fixation point to a second center point, C.sub.r2, of a second area, A.sub.2, defined by Δl.sub.2n and Δr.sub.2.

8. The method according to claim 7, wherein the step of determining the extrusion of 3D-printing material is further based on an intended extrusion of filler material between the intended extrusion of 3D-printing material of the first sector, S.sub.1, with respect to the first sector radius, r.sub.1, of the first sector, S.sub.1, and on an intended extrusion of filler material between the intended extrusion of 3D-printing material of the second sector, S.sub.2, with respect to the second sector radius, r.sub.2, of the second sector, S.sub.2.

9. The method according to claim 1, wherein the luminaire is intended to be at least partially solid, and, in at least one cross-sectional shape of the plurality of cross-sectional shapes, is intended to comprise a plurality of tracks of 3D-printing material.

10. The method according to claim 9, wherein the step of determining the extrusion of 3D-printing material comprises determining a third ratio, R.sub.3, between a first density, ρ1, of 3D-printing material of the first sector, S.sub.1, and a second density, ρ.sub.2, of 3D-printing material of the second sector S.sub.2, such that R.sub.3=r.sub.2.sup.2/r.sub.1.sup.2 is fulfilled, wherein r.sub.1 is the sector radius of the first sector, and r.sub.2 is the sector radius of the second sector, S.sub.2.

11. The method according to claim 1, wherein a fourth ratio, R.sub.4, between a maximum track width, tw.sub.max, and a minimum track width, tw.sub.min, of extruded 3D-printing material, respectively, perpendicular to a direction of extrusion of the 3D-printing material, fulfills R.sub.4<3.

12. The method according to claim 1, wherein a minimum track width, tw.sub.min, of extruded 3D-printing material fulfills 0.1 mm<tw.sub.min<1.6 mm.

13. A 3D-printing apparatus for production of a luminaire via 3D-printing, wherein the luminaire is intended for vertical suspension, comprising a printer head comprising a printer nozzle, configured to extrude a 3D-printing material, and a control system coupled to the printer head for controlling an extrusion of the 3D-printing material, wherein the control system, based on a suspension point of the luminaire, the suspension point being an exterior point of the luminaire by which the luminaire is intended to be vertically suspended, a fixation line through the luminaire, the fixation line elongating from the suspension point and being parallel to a vertical axis, z, and a plurality of cross-sectional shapes of the luminaire along the vertical axis, z, wherein each cross-sectional shape of the plurality of cross-sectional shapes extends in a plane, P, perpendicular to the vertical axis, z, and corresponds to a 3D-printing layer of the luminaire, is configured to, for each cross-sectional shape of the plurality of cross-sectional shapes of the luminaire: a) define a fixation point as the intersection of the fixation line with the cross-sectional shape, b) define a mass balance line in the plane, P, wherein the mass balance line intersects the fixation point, c) define a first side and a second side of the cross-sectional plane with respect to the mass balance line, respectively, wherein the first side and the second side are arranged oppositely each other with respect to the mass balance line, d) define a sector angle, dϕ=180°/n, wherein n is an integer, wherein for each angle ϕ=k.Math.dϕ, wherein k=1, . . . , n e) determine an extrusion of 3D-printing material of the cross-sectional shape as a function of a first sector, S.sub.1, of the sector angle, dck, at the angle, (I), in the first side, wherein the first sector, S.sub.1, is associated with a first mass, m.sub.1, of extruded 3D-printing material, and a second sector, S.sub.2, of the sector angle, &I), at the angle (1)+180°, in the second side, wherein the second sector, S.sub.2, is associated with a second mass, m.sub.2, of extruded 3D-printing material, for minimizing a distance, R.sub.0, between the fixation point and a center of mass, M.sub.t, of the first sector, S.sub.1, and the second sector, S.sub.2, and in case the distance, R.sub.0, exceeds a predetermined threshold distance, R.sub.t, f) define a connection line in the plane, P, intersecting the center of mass, M.sub.t, and the fixation point, wherein, in case the center of mass, M.sub.t, is located in the first side, determine an additional extrusion of 3D-printing material of the cross-sectional shape in the second side such that a first center of mass, M.sub.S1, of the determined additional extrusion of 3D-printing material of the cross-sectional shape of the second side coincides with the connection line in the second side and is located at a first distance, R.sub.S1, from the fixation point, for minimizing |M.sub.S1.Math.R.sub.S1−M.sub.t.Math.R.sub.0|, and wherein, in case the center of mass, M.sub.t, is located in the second side, determine an additional extrusion of 3D-printing material of the cross-sectional shape in the first side such that a second center of mass, M.sub.S2, of the determined additional extrusion of 3D-printing material of the cross-sectional shape of the first side coincides with the connection line in the first side and is located at a second distance, R.sub.S2, from the fixation point, for minimizing |M.sub.S2.Math.R.sub.S2−M.sub.t.Math.R.sub.0|.

14. A computer program comprising computer readable code for causing a computer to carry out the steps of the method according to claim 1 when the computer program is carried out on the computer.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] This and other aspects of the present invention will now be described in more detail, with reference to the appended drawings showing embodiment(s) of the invention.

[0038] FIGS. 1a and 1b schematically show a 3D-printed luminaire that can be provided by the method according to an exemplifying embodiment of the present invention, and

[0039] FIGS. 2-6 schematically show cross-sectional shapes of 3D-printed luminaires that can be provided by the method according to exemplifying embodiments of the present invention.

DETAILED DESCRIPTION

[0040] FIGS. 1a and 1b schematically demonstrate a 3D-printed luminaire 100 from the top, and side views, respectively. A suspension point 110 on the exterior of the luminaire 100 can be seen, from which the luminaire 100 is intended to be vertically suspended by a cord, or rope, or similar, along a fixation line 120. It is intended that when suspended, the luminaire 100 is balanced, such that an opening 101 of the luminaire 100 may be parallel to the x-y plane. In order to achieve this in the context of this invention, a numerical method is used to solve a mass-balance equation (defined more in detail below), e.g. by a computer program, after which a 3D-printer may execute the achieved results for 3D-printing the luminaire 100. For this purpose, initially a 3D shape of the luminaire 100 is defined, which is then divided into a plurality of cross-sectional shapes 130 extending in planes P perpendicular to the z axis. Each of these cross-sectional shapes 130 are intended to represent a single 3D-printed layer of the produced luminaire 100.

[0041] For each cross-sectional shape 130 of the plurality of cross-sectional shapes 130, the intended mass thereof is balanced with respect to a fixation point 140 shown in FIGS. 2 through 5, which is defined as the intersection of the fixation line 120 with the cross-sectional shape 130. For each cross-sectional shape 130, 230 the mass is intended to be distributed in a manner so that the distance R.sub.0 between the fixation point 140 and the center of mass of the luminaire M.sub.t is minimized, preferably equated to zero, so that the mass is balanced with respect to the fixation point 140. Since the extent of which R.sub.0 can be minimized, the mass can be balanced in each cross-sectional shape 130, 230. This is intimately related to the specific 2D shape of that cross-section 130 of the luminaire 100, and there may be a need for additional steps of the numerical method used for solving the mass balance equation for some cross-sectional shapes 130, 230. This is due to that in certain embodiments of the cross-sectional shape 130, 230 the minimized distance R.sub.0 remains larger than a predefined threshold value R.sub.t. Therefore, additional steps may be needed in order to coincide the center of mass M.sub.t with the fixation point 140. In the context of this invention two main approaches are used, the first approach being the main approach, and the second approach comprising the mentioned additional steps in order to achieve the desired minimization of R.sub.0. In the following, for each of the two approaches exemplifying embodiments are given in the remaining figures. The first and main approach is typically sufficient for solving mass balance equations for luminaires 100 with cross-sectional shapes 130 that are quasi-circular such as those shown in FIGS. 2-4, such that the periphery of the cross-section 130 does not intersect itself, and/or any given intersecting line in the plane P, does not intersect the cross-sectional shape 130 in more than two points. For other cross-sectional shapes 230 such as that shown in FIGS. 5 and 6, the second approach is used.

[0042] As mentioned, in general, both approaches are based on solving the mass-balance equation such that a final center of mass M.sub.t of the intended 3D-printing layer coincides with the fixation point 140 of the cross-sectional shape 130, 230.

[0043] For this purpose, a predefined initial 3D-printing material and extrusion width is used for calculating the center of mass M.sub.t, which the 3D-printed layer of that cross-sectional shape 130, 230 would have:

[00001]$\underset{i}{.Math.}{m}_i\left(r_i-R_o\right)=0$

[0044] Wherein R.sub.0 is the distance between the center of mass M.sub.t, and the fixation point 140, m.sub.i represents the mass at every specific location “i” on the cross-sectional shape 130, 230, and r.sub.1 is the distance of that specific location from the fixation point 140. These initial values may be default values stored in a memory system of a computer. Alternatively, they may be values defined by a user for a given luminaire 100. As shown in FIGS. 2-4, a mass balance line 150 is defined in plane P, such that it traverses the fixation point 140 of the cross-sectional shape 130. A first side 160a, and an opposite second side 160b of the cross-sectional shape 130 is defined with respect to the mass balance line 150. An intended extrusion of 3D-printing material is calculated so that the final center of mass M.sub.t would coincide with the fixation point 140. In other words, it is intended that a total effective mass of the first side will equal a total effective mass of the second side, so that a final total center of mass M.sub.t will coincide with the fixation point 140.

[0045] In the following, each of the approaches are described in detail.

[0046] For solving the mass-balance equation according to the first and main approach, an intended extrusion of 3D-printing material is calculated so that the final center of mass M.sub.t would coincide with the fixation point 140. In other words, R.sub.0 will then be close to zero, or equal to zero, so that M.sub.t will be shifted to the fixation point 140. According to the first approach, a sector angle δφ is chosen for the cross-sectional shape 130. This sector angle δφ determines the number steps which the mass-balance equation will be solved. Each step is defined by an angle φ=k.Math.δφ, wherein k=1 . . . , n. Starting from the mass-balance line 150, with k=1 on the first side 160a, a first sector S.sub.1 with a sector angle of δφ is defined. On the second side 160b, and with a mirrored symmetry with respect to the mass-balance line 150, a second sector S.sub.2 is defined symmetrical to the first sector S.sub.1 and with a sector angle of δφ. Each sector S.sub.1, S.sub.2 has a sector radius r.sub.1, r.sub.2, which is defined as the distance of the cross-sectional shape 130 confined by the sector to the fixation point 140. The mass of the first sector S.sub.1 and the second sector S.sub.2 is then balanced with respect to an intended extrusion width, material density, and sector radius of each side. This is repeated for all steps, so that in each step the first sector S.sub.1 is mass balanced with its symmetrical second sector S.sub.2. A few exemplifying embodiments are given in FIGS. 2-4 with different intended structures and 3D-forms of the luminaire 100.

[0047] FIG. 2 demonstrates a cross-sectional shape 130 of the luminaire 100 with a quasi-circular closed loop shape. It is intended that at the cross-sectional shape 130 represents a single track of 3D-printing material 132, meaning that at least that portion of the luminaire 100 defined by this cross-sectional shape 130 is intended to have a single-wall structure. Thus, the mass will be determined by the material density (p), and the extrusion width of the 3D-printing material (tw), also known as the track width in each of the first and second sectors S.sub.1, S.sub.2 of each step. The segment of the cross-sectional shape defined by the first sector S.sub.1 and the second sector S.sub.2 can be defined by a chord, having a chord length Δl.sub.1 and Δl.sub.2, respectively. Consequently, solving the mass balance equation will derive a ratio R.sub.1 between the first and second sector as R.sub.1=tw.sub.1/tw.sub.2=(ρ.sub.2.Math.Δl.sub.2.Math.r.sub.2)/(ρ.sub.1.Math.Δl.sub.1.Math.r.sub.1), wherein tw.sub.1 is the extrusion width of the 3D-printing material in the first sector S.sub.1, and tw.sub.2 is the extrusion width of the 3D-printing material in the second sector S.sub.2. In an embodiment, it may be that one type of material with a given material density is intended to be used for 3D-printing the 3D-printing layer represented by the cross-sectional shape 130. In this case, the material density of the 3D-printing material of the first sector S.sub.1 will be equal to that of the second sector S.sub.2: ρ.sub.1=ρ.sub.2, and thus the mass-balance ratio will be simplified to: R.sub.1=tw.sub.1/tw.sub.2=(Δl.sub.2.Math.r.sub.2)/(Δl.sub.1.Math.r.sub.1). By solving this for each pair of first and second sectors S.sub.1, S.sub.2, the mass will be distributed such that that the final center of mass M.sub.t will coincide with the fixation point 140.

[0048] FIG. 3 depicts a cross-sectional shape 130 of an embodiment of the luminaire 100, wherein at least that portion of the luminaire 100 that is represented by that cross-sectional shape 130 is intended to have a two-wall structure, meaning that a double track of printing material 131, 132 will define the shape of that 3D-printing layer. The space 135 encapsulated in between the first 131 and the second 132 track of the 3D-printing material may be filled by one or more filler materials, such as for instance air, or any other material. Each of the filler materials will have a certain material density, which will be taken into account when balancing the mass of the first sector S.sub.1 and the second sector S.sub.2 for each step. For this purpose, again a first sector S.sub.1 and a symmetrical second sector S.sub.2 will be defined on the first 160a and second 160b sides of the mass-balance line 150 with a sector angle of δφ. The segment of the first track 131 bordered by the first and second sectors S.sub.1, S.sub.2 can be defined by a first inner chord having a first inner chord length of Δl.sub.11 and a second inner chord having a second inner chord length of Δl.sub.21, respectively. The second printing track 132 defined by the first and second sectors S.sub.1, and S.sub.2, will similarly have a first outer chord corresponding to a first outer chord length Δl.sub.12 and a second outer chord corresponding to a second outer chord length Δl.sub.22, respectively. The distance between the first and second printing tracks 131, 132 is given by a radius length Δr.sub.1, and Δr.sub.2 for the first and second segments respectively, and is defined as the length between a center point of the first inner chord length Δl.sub.11 and the center point of the first outer chord length Δl.sub.12, and the length between a center point of the second inner chord length Δl.sub.21 and the center point of the second outer chord length Δl.sub.21, respectively. The material density areas A.sub.1, A.sub.2 confined between the first and second printing tracks 131, 132, and defined by the first and second sectors S.sub.1, S.sub.2, will be taken into consideration in the mass-balance ratio. Assuming that the first and second printing tacks 131 and 132 have a uniform extrusion width around the entire track, then solving the mass balance ratio will result in a ratio R.sub.2 between the density ρ.sub.1 of the filler material in the first sector S.sub.1, and the density ρ.sub.2 of the filler material in the second sector S.sub.2, will be as follows: R.sub.2=ρ.sub.1/ρ.sub.2=(Δl.sub.22.Math.r.sub.2c.Math.Δr.sub.2)/(Δl.sub.12.Math.r.sub.1c.Math.Δr.sub.1), wherein, r.sub.1c is the first sector radius and is defined from the fixation point 140 to a first center point Cr1 in the first area A.sub.1, and r.sub.2c is the first sector radius and is defined from the fixation point 140 to a second center point Cr1 in the second area A.sub.2.

[0049] It is worth noting that, the filler material except for air, will of course also be extruded by the 3D-printer, and the choice of terminology is not meant to convey otherwise.

[0050] It may be that the filler material extruded by the 3D-printer may also comprise multiple printing tracks of filler material. Additionally, or alternatively, the multiplicity of filler material printing tracks may be intended to be deposited according to a predetermined pattern. In these embodiments the density of the filler material may be adjusted by changing the number and/or the track width of the filler material printing tracks in order to achieve the desired mass balance.

[0051] It may be that first printing track 131 and the second printing track 132 can be intended to have the possibility of varying the extrusion widths tw.sub.1, tw.sub.2. In this case, the extrusion width of either or both of the printing tracks 131, 132 can be taken into account in the mass-balance equation.

[0052] Some embodiments of the luminaire 100 may comprise multiple printing tacks, leading to a multi-walled structure. In these luminaires 100, when solving the mass-balance equations in the multiple track cross sections, the density of the filler material confined between each consecutive printing track should be taken into consideration.

[0053] FIG. 4 demonstrates a cross-sectional shape 130 of the luminaire which has a solid mass throughout the entire cross-section 130. In other words, the cross-sectional shape 130 is a plane consisting a plurality of 3D-printing tracks with no spacings, and/or filler material between them. In this embodiment therefore, the extrusion widths tw.sub.1, tw.sub.2 of the first and second sectors S.sub.1, S.sub.2 will not have a significant role in determining the mass of the sectors S.sub.1, S.sub.2, hence will not be considered in the mass-balance equation. Solving the mass-balance equation for this embodiment will lead to a ratio R.sub.3 between the density ρ.sub.1 of the 3D-printing material of the first sector S.sub.1, and the density ρ.sub.2 of the 3D-printing material of the second sector S.sub.2 as follows: R.sub.3=ρ.sub.1/ρ.sub.2=r.sub.2.sup.2/r.sub.1.sup.2, wherein r.sub.1 is the sector radius of the first sector S.sub.1, and r.sub.2 is the sector radius of the second sector S.sub.2.

[0054] It should be noted that within a cross-sectional shape 130, a portion of the cross-sectional shape 130 may be intended to be solid similar to that shown in the embodiment of FIG. 4, while other portions are meant to be single or alternatively multiple walled structures, for instance surrounding the solid structure. Additionally, or alternatively it may be that the space between the walls and/or between the solid structure and the innermost wall is intended to comprise a filler material. In these embodiments, in addition to R.sub.3, R.sub.1, and possibly R.sub.2 need to be taken into consideration when solving the mass-balance equation.

[0055] The first approach may not suffice for achieving the necessary minimization of R.sub.0 for certain embodiments of the luminaire 100 such as those shown in FIGS. 5 and 6. In FIG. 5 for instance, in at least some rotational degrees the luminaire 100 does not have a cross-sectional shape 230 trajectory on which the 3D-printing material may be extruded. Therefore, when dividing the cross-sectional shape 230 into sectors, it is inevitable that some sectors will remain without any substantial cross-sectional portion that is defined by that sector, which would render it impossible to substantiate any intended mass in those sectors in order to mass-balance the two sectors. For these embodiments the second approach is used for balancing the mass such that a final center of mass M.sub.t is defined coinciding with the fixation point 140. In the second approach, similar to the first approach, initially the center of mass M.sub.t is calculated for a given 3D-printing material extrusion width and density. In addition to the sector by sector mass balancing steps of the first approach, depending on the side which with respect to the mass balance line 150 the center of mass M.sub.t falls onto, i.e. the first side 160a, or the second side 160b, additional mass may be provided on the opposite first side 160b, or second side 160a, respectively in order to balance the mass with respect to the fixation point 140. This additional mass will have a secondary center of mass M.sub.S2, or M.sub.S1 on the opposite side first side 160b, or second side 160a, which in order to balance the center of mass M.sub.t such that the final center of mass M.sub.t is defined on the fixation point, is required to be on a connection line 170 which traverses both the fixation point 140 and the original center of mass M.sub.0. An intended extrusion of the 3D-printing material will then be calculated depending on the radius R.sub.S2, or R.sub.S1 of the secondary center of mass M.sub.S2, or M.sub.S1, and the radius of the center of mass from the fixation point: M.sub.S2.Math.R.sub.S2=M.sub.t.Math.R.sub.0, or M.sub.S1.Math.R.sub.S1=M.sub.t.Math.R.sub.0. The calculated intended additional mass 190 will then be distributed equally on either side of the connection line 170 on the side where the secondary center of mass M.sub.S2, or M.sub.S1 is located. This intended additional mass 190 may be intended to be implemented by a larger track width of 3D-printing material, and/or a higher density of material compared to that of the remainder of the cross-sectional shape 230.

[0056] In the embodiment depicted in FIG. 5, the center of mass M.sub.t is located on the first side 160a. The connection line 170 does not traverse any portion of the cross-sectional shape 230 on the second side 160b. Therefore, the additional mass 190 may be distributed equally on either side on the connection line 170 on the second side 160b such that the secondary center of mass M.sub.S2 is located on the second side 160b and on the connection line 170.

[0057] In the embodiment of FIG. 6, the center of mass M.sub.t is again located on the first side 160a. The connection line 170 traverses the cross-sectional shape 230 on the second side 160b. Additionally in this embodiment, it is intended that the secondary mass is distributed such that the secondary center of mass M.sub.S2 falls onto the cross-sectional shape 230. This can be achieved by taking the amount of the original intended mass, and the radius of the original center of mass R.sub.0 into account. Additionally, by defining the distance from the fixation point 140 to the intersection of the secondary mass balance line 150 with the cross-sectional shape 230, as the radius of the second center of mass R.sub.S2, the amount of the intended additional mass can be calculated to be such that it fits the above-mentioned equation. Since the secondary center of mass M.sub.S2 in fact falls on to the cross-sectional shape 230 itself, instead of balancing the intended additional mass on the second side 160b and on either side of the connection line 170, in the embodiment shown in FIG. 6, the additional mass 190 is intended to be extruded on and adjacent to the secondary center of mass M.sub.S2.

[0058] The person skilled in the art realizes that the present invention by no means is limited to the preferred embodiments described above. On the contrary, many modifications and variations are possible within the scope of the appended claims. For example, . . . .

[0059] Additionally, variations to the disclosed embodiments can be understood and effected by the skilled person in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measured cannot be used to advantage.