KR20040011920A - scan conversion unit in tiling-traveresal algorithm and method of the same - Google Patents

Abstract

PURPOSE: A tiling-traversal type scan conversion stage and a method therefor are provided to reduce the necessary cost by applying a manhattan neighbor method and reduce delay of a pipe line by minimizing frequently generated branches. CONSTITUTION: A half-plane edge function is executed to four search points of a stamp and three edges of a triangle(10). All movable directions of the current stamp are obtained based on estimation results of the four search points(20). A final direction is selected by examining stored contexts, a final flag controlling the stored contexts, and tile boundary(30). If up and down contexts are not empty, a stamp stored in the contexts is designated as a stamp to be proceeded next(40).

Description

Scan conversion unit in tiling-traveresal algorithm and method of the same}

The present invention relates to a three-dimensional graphics system, and more particularly, to a high performance pipelined scan conversion unit and method based on a tiling traversal scheme.

In the current 3D graphics field, the demand for a high performance graphics system with enormous computational performance and memory bandwidth is increasing, with the aim of real-time 3D environment, and a high performance scan conversion unit is also an essential element. .

In general, a 3D graphics system is composed of pipelines with distinct roles, which are divided into a geometry processing step and a rasterization step to process a large amount of data.

In this case, the scan conversion stage is located at the top of the rasterization part for obtaining the final pixel value to be output on the screen, and based on the triangle information input from the geometry processing part, several gradient values are obtained. ) And initial pixel fragments.

The general scan conversion unit is composed of triangle set-up, edge processing, and span processing.

Representative algorithms applied to such a scan conversion unit include a scan-line algorithm and a tiling-traversal algorithm.

When the scan-line algorithm is applied (hereinafter, the scan-line method) has been widely used in the initial scan conversion unit because the operation method is clear and simple and easy to configure as a pipeline.

However, a supersampled antialiasing rendering that requires dividing operations on each side of the triangle to compute inverse gradient values and difficult to generate fragments in parallel, creating fragments at several points. In this case, there is a difficulty in the application.

In addition, page crossings occur frequently during rendering, which is a fatal weakness that wastes a lot of memory bandwidth.

In contrast, when applying the tiling-traversal algorithm based on a half-plane edge function (hereinafter, referred to as a tiling-traversal method), it is easy to generate several fragments in parallel using a stamp. It is effective in memory operation by reducing the frequency of page intersections in memory access. In addition, even in the use of the texture cache, it is possible to reduce the hit failure rate to improve performance.

However, a branch frequently occurs in the traversal process of the triangle, and the pipeline is stalled at each time, and thus has a disadvantage of significantly degrading the performance of the pipeline structure.

In order to describe the scan-line method and the tiling-traversal method in detail, the memory efficiency and the texture cache access are described as follows.

First, in terms of memory efficiency, multi-bank DRAMs, which are widely used now, cannot access one row while accessing one row.

Thus, after access to one page is finished, access to the second page in the same bank is attempted, in which case a precharge / row activate command sequence is required.

This prefetch / column activation command sequence occurs when a new page is accessed, but not when a page that has already been opened is accessed.

Therefore, unnecessary cycles of pages are wasteful.

FIG. 1 illustrates a scan-line and tiling-traversal type of memory access, in which a screen is tiled according to a page size of a DRAM.

In the scan-line method, as shown in FIG. 1A, pixels are generated for each scan line, and thus access to several pages occurs frequently.

This results in frequent page crossings and wasteful cycles.

On the other hand, the tiling traversal method generates pixels by tiling (1, 2, 3, 4, 5, 6, 7, 8, 9) as shown in FIG. This results in less page crossings. And while accessing pages in one bank, it is possible to prepare for access to pages in another bank, so that a prefetching effect can be obtained.

That is, since the frame buffer is divided into tiles, as shown in FIG. 1 (b), two banks may be crossed in a checkerboard shape to increase the effect.

If there is little data to be generated in the tile, there is no time for prefetching, which leads to inevitable page crossing. However, even if such a case exists, the tiling-traversal scheme is very effective because the page crossing frequency can be reduced much more than the scan-line scheme.

Next, in terms of the texture cache approach, higher performance is achieved when the tiling-traversal method is applied than the scan-line method.

That is, the tiling-traversal method increases the locality of the texture and lowers the miss ratio of the cache.

Many of the texels required in a fragment can be reused in adjacent fragments, but due to the limited cache space, texel data stored by the cache's replacement strategy is released from the cache after some time.

For example, suppose we use the same texel at the first pixel in two adjacent long spans.

In this case, the scan-line method has a high probability of exiting the texel information in the cache in the middle of the processing process, and the tiling-traversal method has a relatively short time to go to the location, thereby reducing the hit failure rate, thereby improving the performance of the texture cache. It is a great help.

However, the implementation of the semi-plane side function, which is the core operation, requires a lot of cost and considerations, which makes it difficult to implement in hardware. Therefore, it is difficult to find a case where the current tiling traversal method is fully implemented in hardware. .

Accordingly, an object of the present invention is to provide a tiling traversal scan conversion unit and a method implemented in full hardware.

1 is a block diagram illustrating a memory access method of a scan-line method and a tiling-traversal method.

2 is a flow chart of a tiling-traversal pipeline in accordance with the present invention.

3 shows the sign state of the four search points in the stamp when the stamp and triangle intersect according to the present invention.

Figure 4 (a) is a view showing a method for determining the search point sign of the stamp for the three sides of the triangle according to the present invention

4 (b) is a view showing the structure of the side function unit for performing the operation according to Figure 4 (a)

5 is a view showing a portion in which a branch occurs when a triangle is entered according to the present invention;

6 is a detailed view of the triangular set up unit for the scan conversion unit according to the invention.

7 is a detailed view of a tiling-traversal unit for a scan conversion unit according to the invention.

* Explanation of symbols for main parts of the drawings

100: preprocessing unit 200: sample point calculation unit

300: slope calculation unit of three sides 400: incremental value calculation unit

500: half-plane side function calculation unit 600: half-plane side function unit

700: state check unit 800: final direction determination and branch prediction unit

900: Select Select Direction

Features of the scanning conversion method of the tiling traversal method according to the present invention for achieving the above object is the sign of four search points according to the origin, up (RT), down (RB), right (LB) position of the stamp Detecting a, and performing a semi-plane side function operation for each of the three sides of the stamp and the triangle, and combining the determined symbols of the four search points of the stamp two by two, and performs the OR operation If the result is a logical product and the result value is 0, defining the stamp is a non-movable direction; if the result value is 1, the stamp is a movable direction; and based on all the movable directions of the defined stamp, the next step is moved. The final direction is determined by examining the storage context storing the location, the final flag controlling the storage context, and whether the tile boundary has been reached. In step, an input given by the stamp, and then to be makin comprises the step of repeatedly performing the steps:

In this case, the selecting of the final direction may include defining a first priority in a right direction among all movable directions of a stamp, and defining a second priority in a downward direction when the first priority is completed or absent. And, if the second priority is not completed or not, defining the third priority in the upward direction.

A feature of the tiling traversal scanning conversion unit according to the present invention for achieving the above object is a triangle set-up unit, a tiling-traversal unit, a pixel processing unit (pixel) In a scan conversion unit processed by a pipeline of a processing unit, the triangle setup includes a preprocessor for preprocessing information such as coordinates of a triangle, depth, color, transparency, and coordinates for texture mapping, and a floating point in the preprocessor. A sample point calculator that finds an exact pixel that is a coordinate value of a sample point corresponding to three points changed into a fixed point in, and a slope that obtains a slope value of three sides of a triangle connecting the coordinate values of the sample point obtained by the sample point calculator. Increment of the calculation unit and the x-axis of coordinates for depth, color, transparency and texture matching of the pixel And an increment value calculator for calculating an increment value of the y-axis, and a semi-plane edge function calculator for adding an initial adder of only three adders to calculate an initial half-plane edge function value to be used in the tiling traversal unit of the next step. It is.

And the increment value calculation in the increment value calculation unit

,

There are other features to precalculate using equations.

Another feature of the tiling traversal scanning conversion unit according to the present invention for achieving the above object is that the tiling-traversal unit uses Manhattan neighbors to produce a semi-planar side function value of the stamp origin. The pre-processing is performed, and the current stamp is moved with the result of the four points of the stamp obtained from the anti-planar function unit configured to obtain the values of the remaining three points by adding the corresponding increment value to the value. A stamp status checker that checks the possible primitive directions, examines the context contents and tile boundaries and directions stored at the same time, and examines each flag bit to be used when determining the final direction of movement; It is configured to include a final direction determination and branch prediction unit for determining the final direction moved.

The branch predicting unit checks the current tile coordinates and the stamp coordinates currently being processed each time by using a counter to predict in advance which stamp is to be performed next, and the stamp origin stored in the buffer as a result of this prediction is to be performed. Another feature is that the values are sent to the half-plane side function in advance.

The operation according to the characteristics of the present invention is to reduce most of the cost required by applying the Manhattan Naver method, which is a variation of the semi-planar side function, and by applying branch prediction to minimize the number of frequently generated branches The delay of the line can be effectively reduced.

Other objects, features and advantages of the present invention will become apparent from the following detailed description of embodiments taken in conjunction with the accompanying drawings.

A preferred embodiment of a tiling traversal scan conversion unit according to the present invention will be described with reference to the accompanying drawings.

Prior to the description, the specification is based on a 1 pixel wide x 1 pixel high stamp and a 4 pixel wide x 4 pixel high tile.

2 shows a flowchart of a tiling-traversal pipeline according to the present invention.

As shown in FIG. 2, first, a semi-plane side function operation is performed on four search points (origin, RT, RB, LB) and three sides E0, E1, and E2 of a triangle (10).

Next, all the movable directions of the current stamp are obtained based on the evaluation results of the four search points of the stamp (20).

The final direction is determined by checking the final flag, the storage context, and whether the tile boundary is reached based on the obtained result (30).

In this case, the final direction is selected based on the following definitions.

-The right direction is the primary direction.

If the right tile boundary is reached, ignore the right direction and check whether it is possible to move up and down.

In this case, the respective up and down flags are used to determine whether the up and down storage contexts are empty.

At this time, if the up / down context is not empty, a stamp of a position stored therein is designated as a stamp to be processed next. In this case, down is given priority (40).

If the up and down contexts are empty, the right tile context is examined.

If the right tile context is not empty, the stamp of the tile stored therein is designated as a stamp to be processed next. If the right tile context is empty, the triangle processing may be considered as finished. .

The context is a special storage space used in the tiling-traversal method, and is a milestone that stores a position to be moved when branching from the current stamp position to an up direction, a down direction, or another tile.

Therefore, if any one of the up, down and right tile contexts is empty, the value corresponding to the current empty context among the stamp position values in the above (RT), below (RB), and right direction (LB) of the stamp currently being processed. Save it. It is also determined whether or not the stamp to be processed next leaves the current tile.

Referring to the drawings in more detail as follows.

3 is a diagram illustrating the sign state of four search points in a stamp when the stamp and the triangle intersect according to the present invention. 4 (a) is a diagram illustrating a method of determining a search point sign of a stamp for three sides of a triangle according to the present invention, and FIG. 4 (b) is a side function for performing an operation according to FIG. 4 (a). It is a figure which shows the structure of a unit.

As shown in FIG. 3, the sign state of the search point (origin, RT, RB, LB) of the stamp for the three sides of the triangle is detected, and as shown in FIG. Plane side function operation is used to find the sign of the four search points of the current stamp.

At this time, the final sign of each search point is obtained by performing an AND operation on the results of three sides.

As shown in FIG. 4 (b), the validity of the direction flags for the up (RT), down (RB) and right (LB) positions of each stamp is determined based on the symbols of the four search points. do.

In this case, the search points corresponding to each stamp position are ORed, and when the result is 0, it means that the direction cannot be reached. If 1, the direction is valid.

In this way, when the final direction is determined, the pipeline receives the next designated stamp and repeats the above operation.

When the Manhattan Naver method is applied to the tiling-traversal pipeline processing process, the overall operation will be described as follows.

First, to find out whether the four search points of the stamp (origin, RT, RB, LB) are inside or outside the triangle, we need to perform a semi-plane side function.

That is, the calculation part for the origin point (ORIGIN), which is the first search point of the first stamp, is calculated in the setup part. The RT and LB of this stamp are obtained by adding dy and dx to the origin values according to the Manhattan Naver method, and in the case of RB, by adding both dx and dy, the semi-plane side function values for four search points are obtained. Decide

Subsequently, when the determination of the search point is completed, an initial direction of the stamp is obtained. In this case, the flag of the storage context is referred to and a value corresponding to the empty context is stored.

At the same time, the tile boundary is examined and the proposed unit only considers the right and bottom tiles. At this time, it is determined by comparing the row coordinate of the tile with the y coordinate of the RB for each tile boundary, and comparing the column coordinate of the tile with the x coordinate of the RB.

In addition, an up / down flag for controlling the movement of the stamp in the tile is set.

Each flag thus determined is evaluated integrally to determine the final direction of movement.

At this time, the patterns for the respective flag bits are defined in a table and performed accordingly. The values of the corresponding positions to be stored in the context buffer are stored by adding the current context values and inclination values to the respective inclination values. In addition, the flag indicating the state of each storage context is set to 1 when a valid value is stored and to 0 when the stored value is exited.

The value of the storage context at the location to be processed is then entered into the pipeline input.

At this time, since the Manhattan Naver method is applied, RB, LB, and RT values are obtained by adding dx and dy to the value of the current stamp origin, which is calculated and input into the pipeline until the traversal of one triangle is completely completed.

In addition, the tiling-traversal unit is generally responsible for the movement of the stamp. When the general traversal algorithm is applied, the pipeline delay caused by the branching of the stamp movement occurs a lot, which wastes cycles and adversely affects the overall performance.

Therefore, it predicts the processing order of the stamps that need to be visited next time, especially the top, bottom, and right tiles in advance, and inputs the values of the stamps into the pipeline to minimize pipeline delays to maximize pipeline efficiency. To improve.

In general, when a stamp is processed in a tiling-traversal pipeline, the stamp goes to the fragment generation process, and at the same time, the next stamp enters the pipeline input.

It should be noted that the next time the position of the stamp to be determined is determined, the stamp is passed to the fragment generation process.

Therefore, in the general structure that proceeds to the right, when hitting the boundary of the tile or triangle and the branching occurs, there is a problem that the pipeline should be stopped until the current stamp passes through the pipeline stage.

This can be critical to the performance of the entire structure of the pipeline. Experiments in the Quake 3 benchmark in the present invention showed that the branching occurs in about 30% of the total.

In this case, there are two main types of pipeline delay in tiling-traversal. The first is when the stamp hits the tile boundary, and the second is when the stamp is caught on the edge of the triangle. to be.

First, the first stamp hits a tile boundary, which is a pipeline delay caused by hitting the tile boundary as the stamp moves.

In other words, the default movement direction of the stamp is on the right side, but if it hits the tile boundary, the current stamp must be fully processed to know the position of the next stamp. do.

If the second stamp is on the edge of the triangle, the pipeline delay occurs when the edge of the triangle is on the edge of the triangle.

In addition, both cases occur when the stamp touches a tile boundary and encounters a triangle side. Especially for stamps located at the four corners of the tile, it is difficult to avoid pipeline delays.

FIG. 5 is a diagram illustrating a portion where a branch occurs when a triangle is entered. Referring to FIG. 5, it can be seen that a branch occurs at a part of bringing up a context.

Therefore, the branch prediction technique can be used to determine the next stamp position in advance and input it into the tiling-traversal pipeline, thereby minimizing the pipeline stage being empty due to the occurrence of the branch, that is, stopping the pipeline.

In the current tile traversal storage context, the stamp origin information to be processed next is stored. Thus, the key to solving the problem is which of the stored contexts is pipelined immediately after the current context.

At this time, the basic movement direction of the stamp is the right side, and the tiling-traversal unit should continuously apply the information on the right side to the pipeline input.

In FIG. 5, the small square means one stamp, and the number inside the triangle indicates the movement order of the stamp.

The embodiment of the branch prediction scheme will be described in detail with reference to FIG. 5 as follows.

First, when stamp 10 enters the side function operation and is processed and goes to the next step, 11 enters the side function operation step. When stamp 11 enters the side function calculation step, 40 is entered, which is discarded because it is not a valid value.

After the pipeline process for stamp 11 is finished, stamp 12 is imported.

In this case, if the traversal process takes 3 cycles, 2 cycles are wasted, so when the 10th stamp is processed in the side calculation function, the 12th stamp is waited.

In other words, immediately after stamp 11 is processed, stamp 12 can be entered into the pipeline input stage.This means that pipe 11 will be queued to context 12, which is waiting for stamp 11 to finish the transition function and move on to the next stage. It must be entered as a line.

As such, before starting the action, it is necessary to know where the current stamp is in the tile.

To determine the location of the current stamp, the coordinates of the origin of the current stamp and the coordinates of the current tile are compared. At this time, the coordinate values can be easily compared.

For effective hardware implementation, divide the tile size by 2 m x 2 n (where m and n are integers).

The up_position, down_position, and right_position flags are compared with the up / down flags and valid flag values of the storage context.

6 and 7 show a tiling-traversal pipelined scan conversion unit, FIG. 6 shows a detailed view of a triangular set up unit for a scan conversion unit according to the invention, and FIG. A detailed view of the tiling-traversal unit for the scan conversion unit according to the invention is shown.

In the case of implementing a general half-plane side function in hardware, a total of 12 side function units of FIG. 4 (b) are required, and only 24 multipliers and 72 adders are required for this part.

Therefore, this requires a lot of hardware logic (hardware logic) is a problem that the cost required to implement in hardware becomes very large.

This is implemented by applying the Manhattan Naver method as shown in Figure 7, and in order to reduce the cost more effectively, the triangle setup step as shown in Figure 6 was also considered.

In the structure according to the present invention, a total of 15 adders were added to implement the half-plane side function.

6 adds three adders in a general triangular set up unit to perform the first half-plane side function operation.

Referring to FIG. 6, the triangle set-up unit includes a preprocessor 100, a sample point calculator 200, a three-sided slope calculator 300, an incremental value calculator 400 for all triangle information, and the like. And it can be divided into the first half-plane variation function calculation unit 500 per triangle.

The triangle setup preprocessor 100 preprocesses all information of the triangle, that is, coordinates (x, y), depth (z), color (RGB), transparency (α), and coordinates for texture mapping. to be.

Compare unit has three points, V0, V1, and V2, which are input from the geometry processing stage.They are aligned based on y-coordinates so that the uppermost point is vMax, the middle point is vMid, and the lowest point is vMin. Name it.

In Float to Fixed, the coordinates of three points, which are floating point values, are converted into fixed points. This is because, unlike the geometry processing portion that performs floating operations, the rasterization portion performs only integer operations or fixed operations.

In Calculate deltas, the increment value of each side of the triangle, that is, the value of eMax.dx = vMax.dx-vMin.dx, is obtained.

The sample point calculator 200 of each of the three triangle points performs an operation for finding an accurate pixel corresponding to three points changed from a floating point to a fixed point. That is, the y coordinate value of the three vertices of the input triangle is rounded first, and then the adjusted value is obtained using this value and added to the x coordinate values of the three vertices. Become. The sample point is used instead of the vertices that are changed to fixed points in subsequent operations.

The inclination calculator 300 of three sides is a part for obtaining inclination values (Δx / Δy) of three sides of a triangle. Instead of performing a division operation, the operation is performed using a reciprocal LUT (Look Up Table). Because the division operation itself requires a considerable latency, the latency can be reduced by referencing the corresponding portion using a reciprocal lookup table and multiplying the value.

It also has the effect of reducing the size of the rasterization itself. For this reason, in many other cases, we use reciprocal lookup tables instead of division operations.

The increment value calculator 400 of the triangular information calculates an increment value based on the x axis and an increment value based on the y axis of coordinates for depth z, color RGB, transparency α, and texture mapping. . Incremental values are calculations for partial derivatives. The equation is:

,

.

Here C stands for each variable.

Since each piece of information has the same inverse, it can be calculated in advance. By precomputing common values, the hardware implementation can reduce the overhead incurred in incremental calculations.

In this case, the inverse value is calculated in advance as 'oneOverarea'. We also need a division operation, so we are using an inverse lookup table.

The first half-plane variation function 500 is in the case of a tiling-traversal scan conversion unit, and calculates an initial half-plane side function value to be written in a later tiling-traversal unit. to be.

The half-plane side function calculation unit 500 is similar to the oneOverarea calculation portion of the setup unit.

And since this triangle setup unit has 3 cycles of processing capacity, the 'oneOverarea' part is not always used.

Therefore, in order to save additional hardware (especially multipliers), this unit allows oneOverarea to compute the first half-plane function value per triangle while not performing any operation.

In addition, the structure proposed in the present invention adopts the Manhattan Naver method and adds only 15 adders to implement a half-plane side function, thereby more effectively reducing hardware.

As shown in FIG. 7, the tiling-traversal unit may be divided into a semi-plane side function unit 600, a state check unit 700 of the current stamp, a final direction determination unit, and a branch prediction unit 800 according to each operation characteristic. Can be.

The half-plane side function value is obtained by adding only three adders to the triangle setup part.

The checking unit 700 checks the state of the current stamp and checks each flag bit to be used when determining the final moving direction.

First, the raw direction in which the current stamp can move is examined with the result of the four points of the stamp obtained in the semi-plane side function unit 600. At the same time, the contents of the saved context, tile boundaries and orientations are checked.

The final direction determination and branch prediction unit 800 is a part for determining the final direction to move next, based on the result of the stamp checker.

All information values (coordinates (x, y), depth (z), color (RGB), transparency (α), and texture mapping coordinates) corresponding to the origin of the next stamp determined must also be obtained.

To do this, we add the corresponding increments to the information at the current location and store the values in the buffer.

The branch predictor 800 transmits the next stamp value stored in the buffer to the anti-plane side function unit 600 in advance so that the pipeline delay is minimized.

Accordingly, the branch predictor 800 examines the current tile coordinates and the stamp coordinates currently being processed each time by using a counter, and predicts in advance which stamp is to be performed next. And the coordinate values of the corresponding stamp is sent in advance to the semi-plane side function unit 600 to continue the tiling-traversal pipeline until the triangle traversal work is completed.

In addition, the select correct direction (prediction) 900 predicts the final direction in the tiling-traversal unit in advance so that the relationship between the branch predictor 800 and the neighboring parts of the branch predictor 800 which prevents the pipeline delay is prevented. Shows.

As such, the tiling-traversal unit including the branch prediction unit 800 is implemented to effectively reduce the pipeline delay.

As described above, the tiling traversal scan conversion unit according to the present invention applies the Manhattan Naver method, which is a variation of the anti-planar side function, to reduce most of the required cost, and is frequently generated by applying the branch prediction technique. Minimizing the branch effectively reduces pipeline latency by more than 70%.

Those skilled in the art will appreciate that various changes and modifications can be made without departing from the spirit of the present invention.

Therefore, the technical scope of the present invention should not be limited to the contents described in the embodiments, but should be defined by the claims.

Claims (6)

Detects the sign of four search points according to the origin, up (RT), down (RB) and right (LB) positions of the stamp, and performs anti-plane side functions on the three sides of the stamp and triangle, respectively. Steps, Performs an OR operation by combining the determined signs of the four search points of the stamp two by two, and ORs the result of the OR operation, and if the result value is 0, the stamp is in a non-movable direction. Defining it to be a movable direction, Selecting a final direction by investigating a storage context storing a position to be moved next, a final flag for controlling the storage context, whether a tile boundary is reached, and the like based on all movable directions of the defined stamp; And repeating the above steps with the input of the designated stamp. The method of claim 1, wherein selecting the final direction Defining a first priority in a right direction among all movable directions of the stamp; Defining a second priority in a downward direction when the first priority is completed or absent; And a step of defining a third priority in the upward direction if the second priority is not completed or absent. In the scan conversion unit processed by the pipeline of a triangle set-up unit, a tiling-traversal unit, and a pixel processing unit, The triangle setup includes a preprocessor for preprocessing information such as coordinates, depth, color, transparency, and coordinates for texture mapping of the triangle, A sample point calculator for finding an accurate pixel which is a coordinate value of a sample point corresponding to three points changed from a floating point to a fixed point by the preprocessor A slope calculator for obtaining slope values of three sides of a triangle connecting coordinate values of the sample points obtained by the sample point calculator; An increment value calculator for calculating increments based on the x-axis and increments based on the y-axis of coordinates for depth, color, transparency, and texture matching of the pixel; And a half-plane side function calculator for calculating an initial half-plane side function value to be used in the tiling traversal unit of a next step. The method of claim 3, wherein Incremental value calculation in the increment value calculation unit , A tiling traversal scanning conversion unit, which is calculated in advance using an equation. (C generically refers to each variable) The method of claim 1, The tiling-traversal unit is a half-plane function unit configured to preprocess the half-plane side function value of the stamp origin using the Manhattan Naver method, and add the corresponding increment to the value to obtain the values of the remaining three points. Wow, Each flag to be used when determining the final moving direction by examining the raw directions in which the current stamp can move with the result of the four points of the stamp obtained from the anti-planar function, and simultaneously checking the stored context contents and tile boundaries and directions. A stamp status check unit for inspecting bits; And a final predictor and a branch predictor configured to determine a final direction to be moved next based on a result of the stamp state checker. The method of claim 5, wherein The branch predictor examines the current tile coordinates and the stamp coordinates currently being processed each time using a counter to predict in advance which stamp is to be performed in advance, and the stamp origin value to be executed next stored in the buffer as a result of the prediction. The transversal scanning unit of the tiling traversal method, characterized in that for transmitting to the half-plane side function in advance.