A line segment depicting system includes an error discrimination condition memory for designating for each octant an error discrimination condition applied when a DDA (Digital Differential Analyzer) error item is 0.5. First and second different error discrimination conditions are set in the condition memory for first to fourth octants, and for fifth to eighth octants, respectively. A data processing unit receives information of a given line segment and determines in which octant the given line segment is included, and the result of determination is stored in an octant memory, which controls a selector for selecting one of outputs of the error discrimination condition memory. The data processing unit also supplies a DDA parameter to a DDA unit, which sequentially generates a coordinate value (Xn, Yn) of dot positions of an approximate line segment with reference to the error discrimination condition supplied through the selector from the error discrimination condition memory.

Methods and apparatus for rendering a spacial contour texture map onto a generally planar polygon for display on the screen of a video monitor in a computer graphic system includes a memory for storing spacial distance measures between the individual texels of the contour texture map and a boundary on the contour texture map as well as an indentifier flag to define whether the texel is on one side of the boundary or the other. The contour texture map is applied to a modeled polygon by computing the intersection of each direction vector extending from an eyepoint through the center of a selected pixel to the contour texture map in a map space coordinate system. The projected size of a pixel on the contour texture map is also computed. The distance between the intersection point of each direction vector and the boundary of the contour texture map is computed and is projected onto the pixel space, that is, the screen of the display monitor. If the projected distance between the intersection point and the boundary in pixel space is on one side of the boundary, a first texture value is assigned to the pixel for display. If the projected distance from the intersection point to the boundary is on the other side of the boundary then a second texture value is assigned to the pixel. If the distance between the intersection point and the boundary is within a feathering region then a proportion texture value is assigned to the pixel for display on the screen.

A method for removing hidden lines in a two-dimensional surface chart disclosing an image of a three-dimensional surface, includes storing the X, Y and Z co-ordinates of selected points (A, B, C, D, E) of the surface as a first matrix, transforming the first matrix into a second matrix indicating the drawing sequence through the selected points, rotating the points of the second matrix around the Z-axis a first angle .alpha., rotating the second matrix points a second angle .beta. and drawing the two-dimensional surface chart in accordance with the indicated sequence using the X and Y co-ordinate values of the rotated points. The drawing sequence comprises a drawing operation of X-traces, an X-trace being defined as a line passing through points having substantially the same Y values in the first matrix, the drawing operation of one X-trace being followed by a plurality of .DELTA. Y -trace drawing operations between the last drawn X-trace and the next to be drawn X-trace, an Y-trace being defined as a line passing through points having substantially the same X values in the first matrix and a .DELTA.Y-trace being defined as the part of an Y-trace falling between two adjacent X-traces, said sequential drawing operation proceeding in sequence from low Y value X-traces toward high value X-traces. No lines are drawn inside a forbidden area being defined as an area surrounded by an upper horizon and a lower horizon.

A system for displaying graphic images comprising an arrangement for clipping polygons against preselected clipping planes, an arrangement for determining when the vertices of a polygon all lie within one of a number of particular subspaces defined by the clipping planes, and an arrangement for disabling the means for clipping so long as all vertices of a polygon lie in the same subspace.

In order to clip a figure using a predetermined frame, coordinate values of cross points defined by a line segment representing a figure to be clipped and each side of the clipping frame or each extension line thereof are detected. A positional relationship between the line segment and the clipping frame, and the presence/absence of the cross points on the clipping frame are obtained, respectively. By utilizing the above information, a new boundary line which does not exist in a figure before clipping can be extracted. Since the detection of cross point coordinates and the extraction of boundaries are independently processed, high-speed processing can be realized.