Introduction 1962 1934 1950 1987 1993 2003 2005 2008 1979 2002 2004 2007 2003 1999 2002 1999 2000 isotropic anisotropic 1972 2000 2004 2000 1994 The second objective of this review is to identify the frame of reference associated with the haptic oblique effect. This question comes from the observation that the concept of orientation is by definition relative to a set of fixed axes, which define a coordinate system or frame of reference. For example, in the polar coordinate system, an orientation is defined by the angle between some features of the stimulus such as its main axis and an axis of the coordinate system. While the choice of this set of axes can be arbitrary, it is common to choose the vertical and its perpendicular (the horizontal) because of the permanent influence of the vertical gravity force on Earth. In fact, the concept of verticality is so dominant that even in a drawing put on a table that is on a horizontal plane, the verticality is projected as the line belonging to the sagittal plane and perpendicular to the axis of the body. However, the status of verticality must be questioned. In the visual modality, various studies have examined whether the oblique effect was tied to this geocentric reference frame or to a retinocentric frame of reference. In this respect, we will show that the haptic oblique effect observed in the frontal plane is defined in a subjective reference frame that combines ego and geocentric cues. We will also raise the question of which pair of angles is used to code the orientation of a stimulus in space, when the stimuli do not necessarily belong to a plane, where a single angle would suffice to code the orientation. As a matter of fact, it is important to note that different pairs of angles can be used to code an orientation in space in the same way as different coordinate systems can be used to code the position of a point in space. In conclusion, we will argue that the haptic oblique effect occurs at a relatively late stage of orientation processing, when sensory motor traces associated with exploratory movements are transformed into a more abstract representation of the orientation, because the experimental factors that modify the haptic oblique effect's strength either contribute to establishing such a representation (e.g. gravitational cues) or favor its use (e.g., memory constraints). Finally, we will discuss various hypotheses about how the processes involved in the recoding of the sensory-motor traces might yield an anisotropy in the perception or recollection of orientations. Hypotheses on the origins of the oblique effects 2003 1980 2000 2002 2005 2003 1991 1980 2003 2000 2003 1995 1991 1990 1992 1986 2003 1997 2003 2003 1998 1996 1998 1986 1997 1991 1994 2003 2003 2005 2006 2007 Isotropic or anisotropic haptic perception of spatial orientations? Existence of an haptic oblique effect 1976 frontal plane M M M M M M M M 1980 Initial hypotheses on the origin of the haptic oblique effect: the role of prior knowledge and the mode of reproduction of the orientation 1986 1976 1980 1985 1986 1976 1980 horizontal M M M M M M M M 1986 1976 1980 Role of gravitational cues in the haptic oblique effect 1995 1986 1986 horizontal frontal sagittal 1986 M M 1986 M M M M 1995 M M 1986 1995 1996 1991 1996 1996 M M M M Role of previous visual experience and memory in the haptic oblique effect 1978 1997 1998 M M M M 1986 1999 2005 1950 2003 1999 M M M M 1995 1996 M M 1986 1 Table 1 Average absolute errors in the studies of the haptic oblique effect with blindfolded adults Experimental conditions Orientations Oblique effect References Tasks Plane Delay (s) Hand V/H Oblique Difference Reproduction task         Free-time exploration and haptically informed about standard orientations F 0 contra 5 9 4* 1976 Reproduction task         Limited-time exploration (5 s) and haptically informed about standard orientations F 0 contra 4 8.1 4.1* 1980 F 10 contra 4 7.5 3.5* Production task         Free-time production and verbally informed about orientations F 0 one 3.2 8.3 5.1* 1985  Free-time and haptically informed about orientations F 0 one 3.5 8.1 4.6* Reproduction task         Informed H 5 Contra 5 9 * 1986  Uninformed H 5 Contra 5.3 7.5 *   Informed H 5 ipsi 3.5 5.5 *   Uninformed H 5 ipsi 4 4.5 0.5  Reproduction task         Free exploration and uninformed about orientations F 5 contra 5 8 * 1995  F 5 ipsi 5 8 *   S 5 contra 5 8 *   S 5 ipsi 5 8 *   H 5 contra 8.9 12.9 *   Supported exploration H 5 ipsi 6.3 7.8 1.5   Symmetric orientation H 5 contra 7 9.3 *   Symmetric orientation H 5 ipsi 7 9.3 *  Reproduction task         Unsupported exploration H 5 ipsi 3 7 4* 1996  Supported exploration H 5 ipsi 4.7 4.2 −0.5   Normal gravity cues F 5 ipsi 3.5 8.2 *   Reduced gravity cues F 5 ipsi 6.1 7.2 *   Normal S 5 ipsi 3.6 7.1 *   Reduced S 5 ipsi 5.7 7.3 *   Normal H 5 ipsi 5.4 7.3 *   Reduced H 5 ipsi 7.6 9 *  Reproduction task Early and late blind Pooled         Normal F 5 ipsi 5.8 9.9 4.1* 1998  Reduced F 5 ipsi 5.8 9.9 4.1*   Normal H 5 ipsi 7.9 10 2.1   Reduced H 5 ipsi 7.9 10 2.1  Reproduction task         Normal, unoccupied delay F 5 ipsi 3.85 6.8 2.95* 1999  Reduced, unoccupied delay F 5 ipsi 5.5 5.5 0   Normal, unoccupied delay F 30 ipsi 3.85 6.8 2.95*   Reduced, unoccupied delay F 30 ipsi 5.5 5.5 0   Normal, verbal task F 30 ipsi 5.2 8.5 3.3*   Reduced, verbal task F 30 ipsi 5.2 8.5 3.3*   Normal, motor task F 30 ipsi 5.2 8.5 3.3*   Reduced, motor task F 30 ipsi 5.2 8.5 3.3*  Reproduction task         Upright F 5 ipsi 2.5 5.5 3* 2001  Body tilted F 5 ipsi 5 5.5 0.5  Production task         No context, smooth F 5 ipsi 2.3 6.4 4.1* 2005a b  Congruent haptic cues F 5 ipsi 1.4 3.4 2*   Incongruent haptic cues F 5 ipsi 1.8 4.8 3.05*  V/H Oblique Difference Hand Plane Delay first column Haptic orientations defined in a subjective reference frame 1982 1990 Subjective reference frame 1975 1996 1977 Introduction 1967 1993 1995 1999 2001 1982 1997 If the haptic oblique effect is defined in a gravitational reference frame, then the reproduction of the vertical and the horizontal should be more accurate than the reproduction of oblique orientations, regardless of postural conditions. On the other hand, if the haptic oblique effect is defined in an egocentric reference frame, then the reproduction of the two diagonals (45° and 135°), which are parallel and perpendicular to the body tilted to 45° or 135°, should be more accurate than the reproduction of the gravitational vertical and the horizontal, which become oblique in relation to the body. Finally, knowing the effect of tilting the body on the vertical, the SV could constitute a reference axis when the body is tilted. In this case, the reproduction of the SV should be more accurate than all the other orientations in the tilted body conditions. M M M M and also M 1994 1997 2002 2001 and Haptic contextual reference frame 2003 1997 2005a 1994 2002 “Introduction” 1972 2005b M M 2002 M M 2002 1997a b 2002 2003 Haptic orientation in 3D space In all previous experiments, we considered the haptic perception of orientations on a plane rather than in space. An orientation in space is defined by two parameters such as its azimuth and elevation. This observation raises the questions of whether the haptic oblique effect is still present in the absence of any spatial constraint when the participant needs to focus on at least two independent parameters to perform the task. More importantly, given the fact that there is a much larger set of alternative reference frames, which can be used to code an orientation in space than on a plane, the perception of orientations in 3D space raises the question of which reference frame is most adequate to describe the pattern of errors. 2006 2006 On the one hand, the three principal axes were most accurately reproduced when all error components were pooled together. This observation has a straightforward consequence in a “plane-by-plane” analysis, as it implies that the horizontal and vertical axes in the frontal and sagittal planes, as well as the lateral and sagittal axes in the horizontal plane, are more accurately reproduced than the diagonal orientations. In other words, this observation is akin to a demonstration of the classic oblique effect in each one of these planes. Regarding the frontal plane, the results of this experiment were similar to those of the previous experiment. The analysis of the different error components showed a clear oblique effect in both experiments, with the vertical and horizontal orientations being most accurately reproduced, even in the absence of any planar structure in the design of the experiment and of any constraint during the reproduction phase. On the other hand, the presence of the classical oblique effect was much less obvious when we considered the various error components separately. The average angular error inside the horizontal and sagittal planes did not exhibit the expected pattern. Decomposing the in-plane errors in systematic, intersubject and intrasubject error components confirmed this negative finding. Further studies are needed to understand these complex patterns of results observed in 3D space. Let us now look at the ontogenetic development of the haptic oblique effect by comparing it to the corresponding visual one. Developmental aspect of the oblique effects The oblique effects in children and infancy 1975 1978 1984 1973 1992 1973 1992 1995 2002 2008 2004 1996 Subjective-reference frame in infancy 1985 Introduction 2005 2004 2004 This effect of the body tilt on the patterns of results clearly showed that the hypothesis of a purely gravitational reference frame underlying the haptic oblique effect is not supported. Similarly, the results do not favor a purely egocentric reference frame, since a successful haptic discrimination was observed in the body tilted condition both (1) between the 20° oblique rod that was vertical by reference to the body axis in the 20° tilted position and the 30° oblique rod and (2) between the gravitational vertical rod and 10° oblique rod. In summary, the results suggest that spatial orientations are not defined only in a single reference frame. The results indicated that the haptic discrimination of the gravitational vertical (with the 10° oblique) occurred in the two body positions. This result suggests that in tilted position, gravitational vertical seemed still to play the role of a reference axis at least partially. In contrast, the haptic discrimination of the 20° oblique rod depended on the body position. It was absent in the upright position when the 20° oblique rod was oblique by reference to the body axis, whereas it was present in the 20° tilted body position when the 20° oblique rod was vertical by reference to the body axis. This result suggests that, in the tilted position, the egocentric vertical also seemed to have the role of a reference axis, at least partially. 2004 2005 1999 2005a General discussion and perspectives This review of experimental studies of the haptic oblique effect has showed that the perception of spatial orientations can be isotropic or anisotropic depending on various factors such as the presence of gravitational cues, the plane in which orientations are presented, the modality of response (ipsilateral or contralateral hand), etc. One of the most striking findings is the absence of an oblique effect in some conditions, which demonstrates that the haptic system can process all orientations isotropically. This observation stands in sharp contrast with vision where an oblique effect is observed much more systematically, probably because some form of directional anisotropy already emerges at the lowest levels of the visual system. 2001 Haptic orientations defined in a subjective reference frame 1986 1998 1999 1996 2003 2005 2006 2006 2007 1991 2003 Hypotheses on the origins of the oblique effects 2006 1986 1995 1996 1998 1999 1976 1980 1985 2002 2001